CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set 05

SECTION A

Choose and write the correct option in the following questions.

Question. The ratio of volume of a cone and a cylinder of equal diameter and equal height is
(a) 3 : 1
(b) 1 : 3
(c) 1 : 2
(d) 2 : 1
Answer: (b) 1 : 3

Question. A cylinder, a cone and a hemisphere are on the same base and having same height. The ratio of their volumes is
(a) 1 : 2 : 3
(b) 2 : 1 : 3
(c) 3 : 1 : 2
(d) 3 : 2 : 1
Answer: (c) 3 : 1 : 2

Question. The radii of bases of cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3, then ratio between the volumes of cylinder and that of cone is
(a) 8 : 9
(b) 9 : 8
(c) 5 : 7
(d) 7 : 5
Answer: (b) 9 : 8

Solve the following questions.

Question. What is the curved surface area of a right circular cone of height 24 cm and base diameter 14 cm?
Answer: \( 550 \text{ cm}^2 \)

SECTION B

Solve the following questions.

Question. What is the ratio of the volume of a cube to that of a sphere which will fit inside it?
Answer: \( 6 : \pi \)

Question. The internal and external diameters of a hollow hemispherical vessel are 24 cm and 25 cm respectively. If the cost of painting \( 1 \text{ cm}^2 \) of the surface area is Rs. 0.05, find the total cost of painting the vessel all over. \( \left( \text{Take } \pi = \frac{22}{7} \right) \)
Answer: \( 1925.79 \text{ cm}^2 \)

Question. The rain water from a roof of dimensions 22 m \( \times \) 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall (in cm).
Answer: 2.5 cm

Question. A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 100 cm and the diameter of the hemispherical ends is 28 cm. Find the cost of polishing the surface of the solid at the rate of 5 paise per sq. cm.
Answer: Rs. 440

Solve the following questions.

Question. A cylindrical tub, whose diameter is 12 cm and height 15 cm is full of ice cream. The whole ice-cream is to be divided among 10 children in equal ice-cream cones, with conical base surmounted by hemispherical top. If the height of conical portion is twice the diameter of base, find the diameter of conical part of ice-cream cone.
Answer: 6 cm

Question. The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used up on writing 3300 words on an average. How many words can be written in a bottle of ink containing one-fifth of a litre? 
Answer: 480000 words

Question. A cylinder, whose height is two-thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.
Answer: 4 cm

Question. Five hundred persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is \( 0.04 \text{ m}^3 \)?
Answer: 0.5 cm

Solve the following questions.

Question. Water is flowing at the rate of 15km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm? 
Answer: 2 hours

Question. A vessel full of water is in the form of an inverted cone of height 8 cm and the radius of its top, which is open, is 5 cm. 100 spherical lead balls are dropped into the vessel. One-fourth of the water flows out of the vessel. Find the radius of a spherical ball. 
Answer: \( \frac{1}{2} \text{ cm} \)
 

Please click on below link to download CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set E