CBSE Class 8 Mathematics Mensuration Worksheet Set 07

Question. 1. What is the length of the greatest rod that can be placed in a room whose length is \( 10 \text{ m} \), breadth \( 8 \text{ m} \) and height \( 6 \text{ m} \). Given that \( \sqrt{2} = 1.42 \).
(a) \( 13.2 \)
(b) \( 14.2 \)
(c) \( 15.2 \)
(d) \( 16.2 \)
Answer: B

Question. 2. Two cubes, each of edge \( 12 \text{ cm} \) are joined end to end. Find the surface area of resulting cuboid.
(a) \( 1450 \text{ cm}^2 \)
(b) \( 1440 \text{ cm}^2 \)
(c) \( 1420 \text{ cm}^2 \)
(d) \( 1410 \text{ cm}^2 \)
Answer: B

Question. 3. Three cubes whose edges are \( 3 \text{ cm} \), \( 4 \text{ cm} \) and \( 5 \text{ cm} \) respectively are melted to form a single cube. Find the surface area of the new cube.
(a) \( 210 \text{ cm}^2 \)
(b) \( 213 \text{ cm}^2 \)
(c) \( 224 \text{ cm}^2 \)
(d) \( 216 \text{ cm}^2 \)
Answer: D

Question. 4. Three cubes of metal whose edges are in the ratio \( 3 : 4 : 5 \) are melted down into a single cube whose diagonal is \( 12\sqrt{3} \text{ cm} \). Find the edge of smallest of the three given cubes.
(a) \( 6 \text{ cm} \)
(b) \( 7 \text{ cm} \)
(c) \( 8 \text{ cm} \)
(d) \( 9 \text{ cm} \)
Answer: A

Question. 5. If the radius of the base of the right circular cylinder is reduced by \( 50\% \), keeping the same height, what is the ratio of the volume of the reduced cylinder to that of the original.
(a) \( 1 : 9 \)
(b) \( 1 : 8 \)
(c) \( 1 : 4 \)
(d) \( 1 : 2 \)
Answer: C

Question. 6. The radii of the two cylinders are in the ratio \( 2 : 3 \) and their heights are in the ratio \( 5 : 3 \). What is the ratio of their volumes?
(a) \( 20 : 27 \)
(b) \( 18 : 27 \)
(c) \( 15 : 21 \)
(d) \( 11 : 15 \)
Answer: D

Question. 7. The volume of the metallic cylindrical pipe is \( 748 \text{ cm}^3 \). Its length is \( 14 \text{ cm} \) and its external radius is \( 9 \text{ cm} \). Find its thickness.
(a) \( 4 \)
(b) \( 3 \)
(c) \( 2 \)
(d) \( 1 \)
Answer: D

Question. 8. Find the number of coins \( 1.5 \text{ cm} \) in diameter and \( 0.2 \text{ cm} \) thick to be melted to form a right circular cylinder whose height is \( 8 \text{ cm} \) and diameter \( 6 \text{ cm} \).
(a) \( 620 \)
(b) \( 640 \)
(c) \( 660 \)
(d) \( 680 \)
Answer: B

Question. 9. The vertical height of a conical tent is \( 42 \text{ dm} \) and its diameter of the base is \( 54 \text{ dm} \). How many persons can it accommodate if each person is to be allowed \( 2916 \text{ dm}^3 \) of space? \( (\pi = 22/7) \)
(a) \( 11 \)
(b) \( 10 \)
(c) \( 9 \)
(d) \( 8 \)
Answer: A

Question. 10. A piece of metal in the form of a cone of radius \( 3 \text{ cm} \) and height \( 7 \text{ cm} \) melted and cast into a cube. Find the side of cube (nearest to a whole number)
(a) \( 5 \text{ cm} \)
(b) \( 4 \text{ cm} \)
(c) \( 3 \text{ cm} \)
(d) \( 2 \text{ cm} \)
Answer: B

Question. 11. A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surfaces are in the ratio \( 8 : 5 \), what is the ratio of their base to their heights?
(a) \( 3 : 4 \)
(b) \( 5 : 4 \)
(c) \( 6 : 7 \)
(d) \( 9 : 8 \)
Answer: A

Question. 12. Three solid spheres of gold whose radii are \( 1 \text{ cm}, 6 \text{ cm} \) and \( 8 \text{ cm} \) respectively are melted into a single solid sphere. Find the radius of the sphere.
(a) \( 6 \text{ cm} \)
(b) \( 7 \text{ cm} \)
(c) \( 8 \text{ cm} \)
(d) \( 9 \text{ cm} \)
Answer: D

Question. 13. It needs \( 50 \text{ ml} \) paint for painting a picture \( 50 \text{ cm} \times 25 \text{ cm} \). How much paint is needed to paint a similar picture \( 100 \text{ cm} \times 50 \text{ cm} \)?
(a) \( 100 \text{ ml} \)
(b) \( 400 \text{ ml} \)
(c) \( 750 \text{ ml} \)
(d) \( 200 \text{ ml} \)
Answer: D

Question. 14. The sides of a rectangular plot are in the ratio of \( 4 : 3 \) and its area is \( 1452 \text{ m}^2 \). Find the cost of fencing it at Rs \( 2.50 \text{ P} \) per metre.
(a) \( \text{Rs. } 480 \)
(b) \( \text{Rs. } 385 \)
(c) \( \text{Rs. } 375 \)
(d) \( \text{Rs. } 365 \)
Answer: B

Question. 15. How many metres of carpet \( 50 \text{ cm} \) wide will be required to cover the floor of a room \( 30 \text{ m} \times 20 \text{ m} \)?
(a) \( 1000 \)
(b) \( 600 \)
(c) \( 2400 \)
(d) \( 1200 \)
Answer: D

Question. 16. A room is \( 15 \text{ metres} \) long, \( 4 \text{ metres} \) broad and \( 3 \text{ metres} \) high. Find the cost of white washing its four walls at \( 50 \text{ P. per m}^2 \).
(a) \( \text{Rs. } 60 \)
(b) \( \text{Rs. } 57 \)
(c) \( \text{Rs. } 55 \)
(d) \( \text{Rs. } 52 \)
Answer: B

Question. 17. The area of four walls of a room is \( 120 \text{ m}^2 \) and its length is twice the breadth, the height being \( 4 \text{ metres} \). Find the area of the floor.
(a) \( 50 \text{ m}^2 \)
(b) \( 60 \text{ m}^2 \)
(c) \( 75 \text{ m}^2 \)
(d) \( 100 \text{ m}^2 \)
Answer: A

Question. 18. Find the cost of fencing a circular field at the rate of \( 50 \text{ P. per metre} \) if its area is \( 13860 \text{ m}^2 \). \( (\pi = 22/7) \)
(a) \( \text{Rs. } 660 \)
(b) \( \text{Rs. } 540 \)
(c) \( \text{Rs. } 700 \)
(d) \( \text{Rs. } 800 \)
Answer: A

Question. 19. The inside circumference of a circular field is \( 1188 \text{ m} \). A road \( 7 \text{ m} \) wide is constructed on the outside. Find its area.
(a) \( 8070 \text{ m}^2 \)
(b) \( 8270 \text{ m}^2 \)
(c) \( 8370 \text{ m}^2 \)
(d) \( 8470 \text{ m}^2 \)
Answer: D

Question. 20. The area of two circular fields is in the ratio \( 16 : 49 \). If the radius of the latter is \( 14 \text{ m} \), what is the radius of the former?
(a) \( 32 \text{ m} \)
(b) \( 18 \text{ m} \)
(c) \( 8 \text{ m} \)
(d) \( 4 \text{ m} \)
Answer: C

Question. 21. The radii of the two circular field is in the ratio \( 3 : 5 \). The area of the first field is what percent less than the area of the second?
(a) \( 50\% \)
(b) \( 60\% \)
(c) \( 40\% \)
(d) \( 64\% \)
Answer: D

Question. 22. What is the radius of a circular field whose area is equal to the sum of the areas of the three circular fields with radii \( 4 \text{ m}, 4.5 \text{ m} \) and \( 6 \text{ m} \) respectively?
(a) \( 9 \text{ m} \)
(b) \( 10.5 \text{ m} \)
(c) \( 10 \text{ m} \)
(d) \( 8.5 \text{ m} \)
Answer: D

Question. 23. If all the sides of a triangle be increased by \( 200 \text{ percent} \) what is the corresponding increase in its area?
(a) \( 300\% \)
(b) \( 400\% \)
(c) \( 600\% \)
(d) \( 800\% \)
Answer: D

Question. 24. How much paint is required for painting the outer surface of the water tank \( 2 \text{ m} \times 4 \text{ m} \times 3 \text{ m} \) if it needs \( \frac{1}{6} \) of a litre for every \( \text{m}^2 \)?
(a) \( 16 \text{ litres} \)
(b) \( 15 \text{ litres} \)
(c) \( 12 \text{ litres} \)
(d) \( 10 \text{ litres} \)
Answer: C

Question. 25. The edge of three iron cubes are \( 6 \text{ cm}, 8 \text{ cm}, 10 \text{ cm} \) respectively. A new cube was made by melting them. Find the edge of the new cube.
(a) \( 8 \)
(b) \( 12 \)
(c) \( 14 \)
(d) \( 10 \)
Answer: B