## Volume And Surface Area Questions MCQs ### Total Questions : 191

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Question 1. A hollow spherical metallic ball has an external diameter 6 cm and is $$\frac{1}{2}$$ cm thick. The volume of metal used in the ball is :
1.    $$37\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
2.    $$40\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
3.    $$41\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
4.    $$47\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
Question 2. If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cylinder of base diameter 8 cm, then the height of the cylinder is :
1.    4 cm
2.    $$\frac{13}{3}$$ cm
3.    $$\frac{14}{3}$$ cm
4.    5 cm
Question 3. The volume of a right circular cone which is obtained from a wooden cube of edge 4.2 dm wasting minimum amount of wood is :
1.    19404 dm3
2.    194.04 dm3
3.    19.404 dm3
4.    1940.4 dm3
Question 4. The ratio of the volume of a hemisphere and a cylinder circumscribing this hemisphere and having a common base is :
1.    1 : 2
2.    2 : 3
3.    3 : 4
4.    4 : 5
Question 5. If the diameter of a sphere is 6 m, its hemisphere will have a volume of :
1.    $$18\pi$$ m3
2.    $$36\pi$$ m3
3.    $$72\pi$$ m3
4.    None of these
Question 6. The length of the longest rod that can be placed in a room of dimensions 10 m × 10 m × 5 m is :
1.    15$$\sqrt 3$$ m
2.    15 m
3.    10$$\sqrt 2$$ m
4.    5$$\sqrt 3$$ m
Question 7. The sum of the radius and the height of a cylinder is 19 m. The total surface area of the cylinder is 1672 m2, what is the volume of the cylinder ?
1.    3080 m3
2.    2940 m3
3.    3220 m3
4.    2660 m3
5.    2800 m3
Question 8. Given that 1 cu. cm of marble weights 25 gms, the weight of a marble block 28 cm in width and 5 cm thick is 112 kg. The length of the block is :
1.    26.5 cm
2.    32 cm
3.    36 cm
4.    37.5 cm
Question 9. An open box is made by cutting the congruent squares from the corners of a rectangular sheet of cardboard of dimension 20 cm × 15 cm. If the side of each square is 2 cm, the total outer surface area of the box is :
1.    148 cm2
2.    284 cm2
3.    316 cm2
4.    460 cm2
Question 10. V1, V2, V3 and V4 are the volumes of four cubes of side lengths x cm, 2x cm, 3x cm and 4 cm respectively. Some statements regarding these volumes are given below :
(i) V1 + V2 + 2V3 < V4
(ii) V1 + 4V2 + V3 < V4
(iii) 2(V1 + V3) + V2 = V4
Which of these statements area correct ?
1.    1 and 2
2.    2 and 3
3.    1 and 3
4.    1, 2 and 3
Question 11. A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out ?
1.    32 m3
2.    36 m3
3.    40 m3
4.    44 m3
Question 12. The number of circular pipes with an inside diameter of 1 inch which will carry the same amount of water as a pipe with an inside diameter of 6 inches is :
1.    $$6\pi$$
2.    $$12$$
3.    $$36$$
4.    $$36\pi$$
Question 13. If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the reduced cylinder to that of the original one ?
1.    1 : 2
2.    1 : 4
3.    1 : 8
4.    8 : 1
Question 14. The radius of the base and height of a metallic solid cylinder are r cm and 6 cm respectively. It is melted and recast into a solid cone of the same radius of base. The height of the cone is :
1.    9 cm
2.    18 cm
3.    27 cm
4.    54 cm
Question 15. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is :
1.    12π cm3
2.    15π cm3
3.    16π cm3
4.    20π cm3
Question 16. For a sphere of radius 10 cm, What percent of the numerical value of its volume would be the numerical value of the surface area ?
1.    24%
2.    26.5%
3.    30%
4.    45%
Question 17. How many lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm × 11 cm × 12 cm ?
1.    7200
2.    8400
3.    72000
4.    84000
Question 18. A metallic sphere of radius 5 cm is melted to make a cone with base of the same radius. What is the height of the cone ?
1.    5 cm
2.    10 cm
3.    15 cm
4.    20 cm