Surface Area of Combination of Solids - Class 10 Maths MCQ

This set of Class 10 Maths Chapter 13 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
View Answer

Answer: b
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
View Answer

Answer: b
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
View Answer

Answer: a
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
View Answer

Answer: b
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
View Answer

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

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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
View Answer

Answer: c
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)
View Answer

Answer: d
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)
c) Radius of the cylinder + 2(radius of the hemisphere)
d) Height of the cylinder + 2(radius of the hemisphere)
View Answer

Answer: d
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
View Answer

Answer: a
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
View Answer

Answer: c
Explanation: To find the height of the solid we require the height of the cone, height of the cylinder and the radius of the hemisphere.
Height of the solid = height of the cone + height of the cylinder + radius of the hemisphere

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