Volume: Combination of Solids – MCQ

1. There will be total (no. of Qs.) MCQ in this test.
2. Please keep a pen and paper ready for rough work but keep your books away.
3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number.
4. No negative marking for incorrect choice.
5. Please click on “Finish the Test” when you want to exit.
6. All the best – Happy Studying

1. The radius of a cylindrical tank is 28m. If its capacity is equal to that of a rectangular tank of size 28mx16mx11m, then its depth is

4 m

3 m

5 m

2 m

Question 1 of 20

2. The ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube is

π : 8

6 : π

π : 2

8 : π

Question 2 of 20

3. A cone and a cylinder have their heights in the ratio 4: 5 and their diameters are in the ratio 3: 2. The ratio of their volumes will be

6: 7

4: 3

3: 5

5: 3

Question 3 of 20

4. Volume of a hollow right circular cylinder is

πr²h (R² + r²)

πr²h (R² - r²)

πrh (R² - r²)

πh (R² - r²)

Question 4 of 20

5. A container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24 cm and the total height of the container is 16 cm. Its capacity is

5390.60 cm³

5100 cm³

5400 cm³

5425.92 cm³

Question 5 of 20

6. The volume of a sphere (in cu. cm) is equal to its surface area (in sq. cm). The diameter of the sphere (in cm) is

4

3

2

6

Question 6 of 20

7. A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and the heights of the cylindrical and conical portions are 12 cm and 7 cm respectively. The approximate volume of the toy will be

250 cm3

200 cm3

300 cm3

218 cm3

Question 7 of 20

8. A cylinder, a cone and a hemisphere are of equal base and have the same height. The ratio of their volumes is

4: 5: 7

3: 1: 2

1: 2:3

3: 2: 1

Question 8 of 20

9. A spherical steel ball is melted to make 8 new identical balls. Then the radius of each new ball is how much times the radius of the original ball

1/3

1/4

1/2

1/8

Question 9 of 20

10. A river 3 m deep and 10 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

1000 l

10 kl

1000 kl

100 kl

Question 10 of 20

11. A largest sphere is carved out of a cube of side 7cm. The volume of the sphere is

176.42 cu.cm

180.5 cu.cm

179.67 cu.cm

182 cu.cm

Question 11 of 20

12. A cylinder whose height is two thirds of its diameter has the same volume as a sphere of radius 4 cm. The radius of the base of the cylinder will be

4 cm

2 cm

5 cm

8 cm

Question 12 of 20

13. The radii of two right circular cylinders are in the ratio 2: 3 and their heights are in the ratio 5: 4. The ratio of their volumes will be

4: 3

6: 7

5: 9

2: 3

Question 13 of 20

14. A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.

200 cm³

600 cm³

550 cm³

616 cm³

Question 14 of 20

15. The surface area of a cube is equal to the surface area of a sphere. The ratio of their volumes will be

√3 : √4π

π : 3

6 : 5π

√π : √6

Question 15 of 20

16. The volume of a largest sphere than can be cut from cylindrical log of wood of base radius 1 m and height 4 m is:

A

B

C

D

Question 16 of 20

17. A cylindrical vessel of diameter 42 cm and height 40 cm contains water up to a depth of 16 cm. Now a solid iron cylinder, with diameter 14 cm and height 32 cm is placed upright in the cylindrical vessel. The volume of the water required to just submerge the solid cylinder will be

17, 248 cm³

14, 000 cm³

15, 600 cm³

16, 045 cm³

Question 17 of 20

18. A rectangular paper is 44 cm long and 20 cm wide. A cylinder is formed by rolling the paper along its length. The volume of the cylinder will be

3000 cm³

3800 cm³

3050 cm³

3080 cm³

Question 18 of 20

19. A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumes.

1:1:1

2:3:1

3 :1 :2

1:2:3

Question 19 of 20

20. A cylinder and a cone are of same base radius and of same height. The ratio of the volume of cylinder to that of the cone is:

1:2

2:3

3:1

1:3

Question 20 of 20

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