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Surface Area and Volume

⭐MCQs⭐

1. If a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5 cm and height 6 cm, then how much water flows out of the cylindrical cup?
(A) 38.8 cm3
(B) 55.4 cm3
(C) 19.4 cm3
(D) 471.4 cm3

2. Cubical ice cream brick of edge 22 cm is to be distributed among some children by filling ice cream cones of radius 2 cm and height 7 cm up to its brim. How many children will get the ice cream cones?
(A) 163
(B) 263
(C) 363
(D) 463

3. The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
(A) 9.7 cm3 
(B) 77.6 cm3 
(C) 58.2 cm3 
(D) 19.4 cm3

4. A hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 1/8 space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is
(A) 142296 
(B) 142396
(C) 142496
(D) 142596

5. A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form a cone of base diameter 8cm. The height of
the cone is
(A) 12cm 
(B) 14cm
(C) 15cm
(D) 18cm

6. A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is
(A) 21cm
(B) 23cm
(C) 25cm
(D) 19cm

7. A mason constructs a wall of dimensions 270 cm× 300 cm × 350 cm with the bricks
each of size 22.5cm × 11.25cm × 8.75cm and it is assumed that 1/8 space is covered by the mortar. Then the number of bricks used to construct the wall is
(A) 11100 
(B) 11200 
(C) 11000 
(D) 11300

8. Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is
(A) 4 cm
(B) 3 cm
(C) 2 cm
(D) 6 cm

9. If two solid hemispheres of same base radius r are joined together along their
bases, then curved surface area of this new solid is
(A) 4πr2
(B) 6πr2
(C) 3πr2
(D) 8πr2

10. A right circular cylinder of radius r cm and height h cm (h>2r) just encloses a sphere of diameter
(A) r cm
(B) 2r cm
(C) h cm
(D) 2h cm

11. During conversion of a solid from one shape to another, the volume of the new
shape will
(A) increase
(B) decrease
(C) remain unaltered
(D) be doubled

12. Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is
(A) 3 : 4
(B) 4 : 3
(C) 9 : 16
(D) 16 : 9


⭐True / False⭐

1. If a solid cone of base radius r and height h is placed over a solid cylinder having same base radius and height as that of the cone, then the curved surface area of the shape is πr√(h2+r2) + 2πrh

2. A spherical steel ball is melted to make eight new identical balls. Then, the radius of each new ball be (1/8)th the radius of the original ball.

3.Two identical solid cubes of side a are joined end to end. Then the total surface area of the resulting cuboid is 12a2.

4. Total surface area of a TOP (lattu) is the sum of total surface area of hemisphere and the total surface area of cone.

5. A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball
is (4/3)πa3



1. (A) 2. (C) 3. (D) 4. (A) 5. (B) 6. (A) 7. (B) 8. (C) 9. (A) 10. (B) 11. (C) 12. (D) 13. 
1. T 2.) F, r/2 3.) F, 10a^2 4.) F 5.) F, (1/6)πa^3
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