CBSE Class 9 Mathematics Surface Areas And Volumes Worksheet Set A

Read and download free pdf of CBSE Class 9 Mathematics Surface Areas And Volumes Worksheet Set A. Students and teachers of Class 9 Mathematics can get free printable Worksheets for Class 9 Mathematics Chapter 13 Surface areas and Volumes in PDF format prepared as per the latest syllabus and examination pattern in your schools. Class 9 students should practice questions and answers given here for Mathematics in Class 9 which will help them to improve your knowledge of all important chapters and its topics. Students should also download free pdf of Class 9 Mathematics Worksheets prepared by school teachers as per the latest NCERT, CBSE, KVS books and syllabus issued this academic year and solve important problems with solutions on daily basis to get more score in school exams and tests

Worksheet for Class 9 Mathematics Chapter 13 Surface areas and Volumes

Class 9 Mathematics students should refer to the following printable worksheet in Pdf for Chapter 13 Surface areas and Volumes in Class 9. This test paper with questions and answers for Class 9 will be very useful for exams and help you to score good marks

Class 9 Mathematics Worksheet for Chapter 13 Surface areas and Volumes

Case study question- 1

An antique box and its dimensions excluding the stand is given below.

""CBSE-Class-10-Mathematics-Surface-Areas-and-Volumes-1

Question. What is the volume of the jewellery box?
a) (𝑙×𝑏×ℎ) + 𝜋𝑟2
b) (𝑙×𝑏×ℎ) + 1/2 𝜋𝑟2
c) 2(𝑙𝑏×𝑏ℎ × 𝑙ℎ)+𝜋𝑟2
d) (𝑙×𝑏×ℎ) + 2𝜋𝑟ℎ
Answer : B

Question. How much brass will be needed to plate the curved surface of the dome as shown in figure?
a) 1320cm2
b) 220 cm2
c) 440 cm2
d) 660 cm2
Answer : D

Question. How many sheets of dimensions 14cm x 30cm x 2cm can be placed in the box?
a) 10
b) 5
c) 2
d) 15
Answer : B

Question. Considering the thickness of the box to be negligible, how much velvet cloth will be needed to cover the cuboidal inner area?
a) 1720 cm2
b) 880 cm2
c) 1300 cm2
d) 1580 cm2
Answer : C

 

Very Short Answer type Questions

Question. A circus tent is cylindrical up to a height of 3m and conical above it. If the diameter of the base is 105m and the slant height of the conical part is 53cm, find the total canvas required in making the tent.
Answer : 9735m2

Question. A bird-bath in a garden is in the shape of a cylinder with a hemi-spherical depression at one end. The height of the hollow cylinder is 1.45m and its radius is 30cm. find the TSA of the bird-bath.
Answer : 3.3m2

Question. The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder
Answer : 4620 cm3

Question. Two cubes each of side 4cm are joined end to end. Find the volume of the resulting solid.
Answer : 
128cm3

Question. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
Answer : 
9units

Question. A metallic cylinder has radius 3cm and height 5cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole is drilled in the cylinder. The conical hole has a radius of 3/2 cm. and its depth is 8/9cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in the conical shape.
Answer : 133: 2

Question. A rectangular sheet of paper 30cm x 18cm can be transformed into the curved surface of a right circular cylinder in two ways either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volume of the two cylinders thus formed.
Answer : 5:3

Question. Find the volume of a right circular cylinder of base radius 7 cm and height 10 cm.
Answer : 
1540 cm3

Question. A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the ratio between the radius of their bases to their heights is 3:4
Answer : 3:4

Question. The internal and external diameters of a hollow hemispherical vessel are 12cm and 16cm respectively. If the cost of painting 1 sq.cm of the surface area is Rs. 5, find the total cost of painting the vessel all over. (π = 3.14)
Answer : 
Rs. 3579.60

Question. The sum of the radius of the base and height of a solid right circular cylinder is 37cm. if the total surface area of the solid cylinder is 1628 sq.cm, find the volume of the cylinder. (π= 22/7)
Answer : 
4620 cub.cm

Question. An ice - cream cone consists of a cone surmounted by a hemisphere. The radius of the hemisphere is 3.5 cm and height of the ice - cream cone is 12.5 cm. Calculate the volume of the ice – cream in the cone.
Answer : 205.33 cm3

Question. From a solid cylinder of height 14 cm and base radius 7 cm, two identical conical holes from each end of radius 2.1 cm and height 4 cm are drilled out. Find the volume of the remaining solid.
Answer : 2119.04 cm3

 

1. The dimensions of a cuboid are in the ratio 3:2:2 and the lateral surface area of cuboid is 2000m2. The outer surface of the cuboid is painted with coloured enamel at the rate of Rs 8 per m2. Find the total cost of painting the outer surface of the cuboid.

2. The floor of a cuboidal hall has perimeter equal to 250 m and height 6m. Find the cost of painting its four walls (including doors etc) at the rate of Rs 8 per m2

3. Gopal sweets placed an order of making 30cm x 20cm x 6cm cardboard boxes for packing their sweets. For all overlaps, 4% of total area is required extra. If cost of the cardboard is 25p for 100 cm2, find the cost of the cardboard used for making 1000 boxes.

4. Food Corporation of India stacks bags containing wheat in the shape of cuboidal blocks in an open field on wooden platform and these blocks are covered with tarpaulin. If there be 10 blocks, each having dimensions 10m x 5m x 3m, then find the cost of the tarpaulin used to cover these blocks at the rate of Rs 12.5 per m2. Assuming that there is negligible wastage of tarpaulin in folds.

5. The diameter of a road roller is 140cm and its length is 2.2m. It takes 400 complete revolutions to move once
over to level a stretch of road 2.2m wide. Find the surface area of the stretch of road leveled in m2. (Take π = 22/7)

6. A closed cylindrical water tank is made from a plastic sheet. Its diameter is 1.4m and height 3.5m. Find
(i) Lateral (curved) surface area of the tank.
(ii) The actual area of the plastic sheet used if 1/13 of sheet actually used was wasted in making the tank. (Take π = 22/7)

7. There are 50 students in class X of a school. Class teacher asks all the students to prepare cylindrical container with a base at the bottom but open at the top, using cardboard. Each student has to make one container of radius of 4.2cm and height 11.2 cm. the class teacher will provide the cardboard to all the students. The cardboard is purchased by the teacher from the market at the rate of Rs 10 per 100 cm2. Find the amount spent by the class teacher for the purchase of the cardboard.

8. The radius of the base of a conical tent is 12m the tent is 9m high. Find the cost of canvas required to make the tent, if one square metre of canvas costs Rs 120. (Take π = 22/7)

9. A conical tent is made of tarpaulin 1.5m wide. Vertical height of the conical tent is 4m and base diameter is 6m.
Find the length of the tarpaulin used, assuming that 10% extra material is required for stitching margins and wastage in cutting. (Take π = 3.14)

10. Along a highway 50conical pillars are constructed. Each pillar has base diameter 28 cm and vertical height 18cm. find the total cost of painting these pillars at the rate of Rs. 120 per m2. (Take π = 22/7)

11. The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7m. Find the area available to the motorcyclist for riding. (Take π = 22/7)

12. A hemispherical bowl made of brass, 0.2cm thick. The inner radius of the bowl is 4cm. find the outer curved surface area of the bowl. Also find the cost of carving its outer surface at the rate of Rs 2 per cm2. (Take π = 22/7)

13. A right circular cylinder just encloses a sphere (see figure). If the height of the cylinder is 21cm, then find the surface area of cylinder (Take π = 22/7)

""CBSE-Class-9-Mathematics-Surface-Areas-And-Volumes-Worksheet-Set-B

14. A hemispherical dome, open at base, is made from a sheet of fibre, if radius of hemispherical dome is 40cm and 13 / 170 of fibre sheet actually used was wasted in making the dome, then find cost of the dome at the rate of Rs 35 per 100 cm2. (Take π =3.14)

15. A cuboidal water tank is 5.6 m long, 3.5 m wide and 4m deep. All these dimensions are of the interior of the tank. Find in litres, the capacity of the tank. (Take 1m3 capacity = 1000 l of water)

16. A cuboidal water tank is filled by tap water at the rate of 1.2 litres per second. Find the length of an edge of the tank in centimeters if the tank is completely filled in 24 minutes.

17. A godown measures 30m x 20m x 8m. Find the maximum number of wooden boxes each measuring 1.2m x 0.8m x 0.5m that can be stored in the godown.

18. A village has a population of 5400. 60 litres of water is required per person per day. The village has water tank measuring 48m x 27 m x 5m completely filled with water. For how many days the water of this is sufficient?

19. A river 3.5 m deep and 28m wide is flowing at the rate of 2.4 km per hour. How many litres of water will flow into the sea in 10minutes? (1m3 = 1000 litres of water).

20. Coins of same size are placed one above the other and a cylindrical block is formed. The volume of the block is 49.28 cm3. If diameter of each coin be 2.8cm and thickness 0.2m, then find the number of coins arranged in block. ( π = 22/7)

21. Water is supplied to a city population for general use (not for drinking) from a river through a cylindrical pipe. The radius of the cross section of pipe is 10 cm. the speed of water through the pipe is 18 km per hour. Find the quantity of water in litres which is supplied to the city in two hours. (π = 3.14 and 1m3 = 1000l)

22. At a mela a stall keeper in one of the food stalls has a large cylindrical vessel of base radius 15cm filled to the height of 32 cm with orange juice. The juice is filled in small cylindrical glasses of radius 3cm upto a height of 8 cm and sold for Rs 3 each. How much money the stall keeper receives after selling the juice completely?

23. A cylindrical reservoir 12 m deep is plastered from inside the lateral surface with concrete mixture. The finished inside surface is measured and the payment is made at the rate of Rs. 15 m2. if the total payment made is of Rs 5652, then find the capacity of this reservoir in kilolitres. (Take π = 3.14)
24. The capacity of a closed cylindrical vessel of height 84 cm is 26.4 litres. How many square metres of metal is required to make seven such vessels. (π = 22/7)

25. A cylindrical groove is made in a cylindrical 21 cm long solid piece of wood. The groove is filled with lead and this cylindrical lead block is of same length as that of the wooden cylinder is 3 cm and the outer diameter of the wooden cylinder is 12 cm, find the volume of the wood and that of the lead. (π = 22/7)

26. Some soft drink is served to 40guests in a party. Each guest is served drink, one and only one time in same size of conical glass and the same quantity to each. AB = 6cm is the diameter of the base of the soft drink cone in the conical glass and the depth of this cone is 5cm. find the quantity of the soft drink in litres which is just sufficient for 40 guests. (π = 3.14)

27. The diameter of the top of a conical reservoir is 4.5m and depth 14m. Find the capacity of the reservoir in kl. (π = 22/7)

28. The volume of the space inside a right circular conical tent is 22 m3 and its vertical height is 3m. Find the curved surface area of the conical tent. ((π = 22/7)

29. A heap of wheat is in the form of a cone of vertical height 3m and volume 86.625 m3. The heap is to be covered by a sheet of canvas. Find the area of the canvas which is just sufficient to cover the heap. (π = 22/7)

30. A shot put is a metallic sphere of radius 4.9 cm. if the density of the metal is 7.8g per cm3, find the mass of the shot put (π = 22/7)

31. There are 42 hemispherical bowls, each of radius 3.5 cm. find the quantity of water in litres which is just sufficient to fill these 42 bowls. (π = 22/7)

32. find the volume of a sphere whose surface area is 55.44 cm2 (π = 22/7)

33. If the solid sphere of diameter 8.4 cm be immersed in a tub full of water, find the amount of water displaced by the solid sphere.

34. A hemispherical dome is constructed of a metallic sheet 1cm thick, if the inner radius is 99 cm, then find the volume of the metal sheet used. (π = 22/7)

35. 64 solid metallic spheres, each of radius 0.15cm are melted to form a single bigger sphere. Find radius of the bigger sphere.

1. The curved surface area of a cylinder of height 21cm is 660cm2 ,find its radius. (r = 5cm)

2. The Volume of a cylinder is 448 π cm3 and height 7 cm. Find its total surface area. (754.28cm2)

3. The volume of a sphere is 905 1/7 cm3. Determine its diameter. (12cm)

4. If the volume of a sphere is 36 π cm3, then find its radius (3 cm)

4. The outer diameter of a spherical shell is 10 cm and inner diameter is 9cm. Find the volume of the metal contained the shell (141.95cm3)

5. the length, breadth and height of a room are 5 m, 4m and 3m. Find the cost of colour washing its four walls and ceiling at the rate of Rs 7.50 per square metre. (Rs 555)

6. Three cubes each of 5cm edge are joined end to end. Find the surface area of the resulting Cuboid (350 sqcm)

7. Two cubes of side 6 cm each joined end to end. Find the surface area of the resulting cuboid. (360cm2)

8. The radii of two right circular cylinders are in the ratio 2:3 and their heights are in the ratio 5:4 Calculate the ratio of their curved surfacearea (5:6)

9. How many metres of cloth 5m wide will be required to make a conical tent, the radius of whose base 7m and height 24m? (110m)

10. The outer and inner diameters of a hemispherical bowl are 17cm and 15cm find the cost of polishing it over at 25 paise ( Rs 25.14) percm2

11. A river 2m deep and 30m wide is flowing at the rate of 2km per hour. How much water will fall into the sea in a minute (2 000m3)

12. The volume of a cube is 125cm3. Find its surface area (150cm2)

13. Find the length of the longest pole that can be put in a room of dimensions 6m x 6m x 3m (9m)

14. The surface area of a sphere is 5544cm2, find its diameter. (42 cm)

15. The sum of the radius of the base and height of a cylinder is 37m. If the total surface area of the Solid cylinder is 1628m2, find the volume of cylinder (4620m3)

16) A hemispherical bowl is made of steel 0.25cm thick .The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl. (173.25 cm2)

17) The ratio of the CSA to the TSA of a right circular cylinder is 1: 3. Find the volume of the cylinder If its T S A is 1848cm2 (4312 cm2)

18) The diameter of a roller, 120cm long is 84cm. It takes 500 complete revolutions to level a Playground. Find the cost of leveling it at the rate of Rs 25 per sq metre. (Rs 39,600)

19) The height of a cone is 15cm. If its volume is 1570 cm3, find the radius of the base. (π = 3.14) (r = 10cm)

20) Find the surface area of a sphere whose volume is 99/7 cm3 (r = 1.5cm, SA= 198/7cm2)

21) The total surface area of a solid hemisphere is 1848cm2. Find the volume of the hemisphere. (5749.3 cm3)

22) A hemispherical bowl of internal radius 9cm is full of a liquid. This liquid is to be filled into Small cylindrical bottles of diameter 3cm and

height 4cm each. Find the minimum number Of bottles required to empty the bowl (54) 23) Curved surface area of a cylinder is 4400cm2 the circumference of its base is 110 cm.Find the height of the cylinder ( 40 cm)

23. Base circumference of a cylinder is 132 m and its height is 2m. Find its curved surface area (264m2) 24) Three solid spheres of iron whose diameters are 2cm, 12cm and 16cm respectively are melted Into sphere. Find the radius of the new sphere (9 cm)

25) The radius and height of a cylinder are in the ratio 2:3. If the volume of a cylinder is 1617cm3 Find its radius and height (7 cm, 10.5 cm)

26) A solid cube of side 12 cm is cut into 8 cubes of equal volumes. Find the side of new cube (6 cm)

27) The paint in a certain container is sufficient to paint an area equal to 9.375 sqm. How many bricks of dimensions 22.5cm x 10cm x 7.5cm container can be painted out of this? (100)

28) Find the total surface area of the cone whose base radius is 8cm and sum of base radius and slant height is 21cm (528 sqcm)

29) The height of a rectangular room is 2.5m. The cost of painting its four walls at the rate of Rs. 20/m2 is Rs.2500. Find the perimeter of the room (50m)

30) A cone and cylinder are having equal base radius. Find the ratio of the heights of cone and cylinder if their volume is equal

31) The radius of sphere is 5cm. If the radius is increased by 20%. Find how much percent volume is increased

32) The radius of a spherical balloon is inflated from 1.5 cm to 2.5 cm by pumping more air in it. Find the ratio of surface Area of resulting balloon to the original balloon

33) The curved surface area and volume of a cylindrical pillar are 264cm3 and 396cm3.. Find the diameter and height of the pillar

34) A right circular cone is 5.4cm high and radius of its base is 2cm. It is melted and recast into another right circular cone with radius of base as 1.5 cm. Find the height of the new cone formed

35) If the volume of a sphere is divided by its surface area then the result is 27. Find the radius of sphere

36) Total cost of making a cylindrical pipe is Rs 7040 at the rate of Rs 5 per cubic meter, if the height of cylindrical pipe is 7m then find its radius (8m)

37) A well of diameter 8 m is dug out up to 7 m. Calculate the volume of the earth dug out (392 m3)

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CBSE Class 9 Mathematics Chapter 13 Surface areas and Volumes Worksheet

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