# Mathematics Questions and Answers – Surface Area and Volume of Combination of Solids – 1

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Surface Area and Volume of Combination of Solids – 1”.

1. A solid is in the form of a cone mounted on a hemisphere. The radius and height of the cone are 3 m and 4 m. Find the surface area of the given solid.
a) 114.4 m2
b) 103.62 m2
c) 70 m2
d) 72.5 m2

Explanation: Slant height = $$\sqrt {h^2 + r^2}$$
= $$\sqrt {4^2 + 3^2}$$
= √25
= 5 m
The surface area of the toy = C.S.A of the cone + C.S.A of the sphere
= πrl + 2πr2
= (3.14 × 3 × 5) + (2 × 3.14 × 32)
= 47.1 + 56.52
= 103.62 m2

2. Two cubes each of volume 27 cm3 are joined together. Find the surface area of the resulting solid?
a) 109.4 cm2
b) 126 cm2
c) 150 cm2
d) 189.4 cm2

Explanation: Volume of cube = a3 = 27
a = 3 cm
Joining 2 cubes results in a cuboid. Length of the cuboid (l) = 3 + 3 = 9 cm
Height of the cuboid (h) = 3 cm
Breadth of the cuboid (b) = 3 cm
Surface area of cuboid = 2(lb + bh + hl) = 2(27 + 9 + 27) = 126 cm2

3. A medicine capsule is in the form of a cylinder with two hemispheres joined together at the ends. Find the surface area if the length of the capsule is 14 mm and the width is 5 mm.
a) 219.8 mm2
b) 105 mm2
c) 115.4 mm2
d) 317.2 mm2

Explanation: Radius of the common base (r) = 2.5 mm because the width of the capsule is equal to the diameter of the cylinder.
Length of the cylinder (h) = length of the capsule – 2(radius of the hemisphere) = 14 – 2(2.5) = 9 mm
The surface area of the capsule = C.S.A of the cylinder + 2(C.S.A of the hemisphere)
= 2πrh + 2(2πr2)
= (2 × 3.14 × 2.5 × 9) + 2(2 × 3.14 × 2.52)
= 219.8 mm2

4. A solid is in the form of a cone mounted on a hemisphere. The radius and height of the cone are 3 m and 4 m. Find the volume of the given solid?
a) 93.21 m3
b) 94.21 m3
c) 84.21 m3
d) 82.21 m3

Explanation: Volume of the solid = volume of the cone + volume of the hemisphere
= $$\frac {1}{3}$$πr2h + $$\frac {2}{3}$$πr3
= ($$\frac {1}{3}$$ × 3.14 × 32 × 4) + ($$\frac {2}{3}$$ × 3.14 × 33)
= 94.21 m3

5. What is the length of the resulting solid if two identical cubes of side 8 cm are joined end to end?
a) 26 cm
b) 16 cm
c) 21 cm
d) 14 cm

Explanation: Length of resulting cuboid = 2 × side of the cube
= 2 × 8 cm
= 16 cm

6. Two cubes each of volume 64 cm3 are joined together. Find the volume of the resulting solid?
a) 152.76 cm3
b) 154 cm3
c) 256 cm3
d) 141.76 cm3

Explanation: Volume of cube = a3 = 64
a = 4 cm is the side of each cube.
Joining 2 cubes results in a cuboid. Length of the cuboid (l) = 4 + 4 = 16 cm
Height of the cuboid (h) = 4 cm
Breadth of the cuboid (b) = 4 cm
The volume of the cuboid = lbh = 16 × 4 × 4
= 256 cm3

7. What is the skeletal formula to find the T.S.A of the tank consisting of a circular cylinder with a hemisphere attached on either end?
a) 2πrh + 2(2πr3)
b) 2πrh + 2(πr2)
c) 2πrh + 2($$\frac {2}{3}$$πr2)
d) 2πrh + 2(2πr2)

Explanation: T.S.A of the tank = C.S.A of the cylinder + 2(C.S.A of the hemisphere)
= 2πrh + 2(2πr2)

8. What is the formula to find the height of the tank consisting of a circular cylinder with a hemisphere attached on either end?
a) Radius of the cylinder + 2(height of the hemisphere)
b) Height of the cylinder + 2(height of the hemisphere)
d) Height of the cylinder + 2(radius of the hemisphere)

Explanation: To find the height of the tank consisting of a circular cylinder with a hemisphere attached on either end requires the height of the cylinder and radius of the hemisphere.
Height of the tank = height of the cylinder + 2(radius of the hemisphere)

9. What is the C.S.A of resulting solid if two identical cubes are joined end to end together with the length of the sides of the cube is 4 m?
a) 160 cm2
b) 205.6 cm2
c) 168.23 cm2
d) 604 cm2

Explanation: Cuboid is the resulting solid when two identical cubes are joined end to end together.
Length of the cuboid (l) = 4 + 4 = 16 cm
Height of the cuboid (h) = 4 cm
Breadth of the cuboid (b) = 4 cm
The curved surface area of cuboid = 2h(l + b) = (2 × 4)(16 + 4)
= 160 cm2

10. What is the formula required to find the height of a solid in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end?
a) 4793 m3
b) 2763 m3
c) 2783 m3
d) 4783 m3