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 m^{2}

b) 103.62 m^{2}

c) 70 m^{2}

d) 72.5 m^{2}

View Answer

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 + 2πr

^{2}

= (3.14 × 3 × 5) + (2 × 3.14 × 3

^{2})

= 47.1 + 56.52

= 103.62 m

^{2}

2. Two cubes each of volume 27 cm^{3} are joined together. Find the surface area of the resulting solid?

a) 109.4 cm^{2}

b) 126 cm^{2}

c) 150 cm^{2}

d) 189.4 cm^{2}

View Answer

Explanation: Volume of cube = a

^{3}= 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 cm

^{2}

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 mm^{2}

b) 105 mm^{2}

c) 115.4 mm^{2}

d) 317.2 mm^{2}

View Answer

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(2πr

^{2})

= (2 × 3.14 × 2.5 × 9) + 2(2 × 3.14 × 2.5

^{2})

= 219.8 mm

^{2}

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 m^{3}

b) 94.21 m^{3}

c) 84.21 m^{3}

d) 82.21 m^{3}

View Answer

Explanation: Volume of the solid = volume of the cone + volume of the hemisphere

= \(\frac {1}{3}\)πr

^{2}h + \(\frac {2}{3}\)πr

^{3}

= (\(\frac {1}{3}\) × 3.14 × 3

^{2}× 4) + (\(\frac {2}{3}\) × 3.14 × 3

^{3})

= 94.21 m

^{3}

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

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

= 2 × 8 cm

= 16 cm

6. Two cubes each of volume 64 cm^{3} are joined together. Find the volume of the resulting solid?

a) 152.76 cm^{3}

b) 154 cm^{3}

c) 256 cm^{3}

d) 141.76 cm^{3}

View Answer

Explanation: Volume of cube = a

^{3}= 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 cm

^{3}

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(2πr^{3})

b) 2πrh + 2(πr^{2})

c) 2πrh + 2(\(\frac {2}{3}\)πr^{2})

d) 2πrh + 2(2πr^{2})

View Answer

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

= 2πrh + 2(2πr

^{2})

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

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 cm^{2}

b) 205.6 cm^{2}

c) 168.23 cm^{2}

d) 604 cm^{2}

View Answer

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 cm

^{2}

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 m^{3}

b) 2763 m^{3}

c) 2783 m^{3}

d) 4783 m^{3}

View Answer

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

**Sanfoundry Global Education & Learning Series – Mathematics – Class 10**.

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