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10 circular plates each of thickness 3 cm, each are placed one above the other and a hemisphere of radius 6 cm is placed on the top just to cover the cylindrical solid. What is the volume of the solid so formed?

A) 264 \( \Large \pi cm^{3} \)
B) 252 \( \Large \pi cm^{3} \)
C) 236 \( \Large \pi cm^{3} \)
D) None of these

Correct Answer:




D) None of these

Description for Correct answer:
If 10 Circular plates each of thickness 3 cm, each are placed one above the other, then it forms a cylinder with height \( \Large \left(3 \times 10 = 30 cm\right) \) and a hemisphere of radius 6 cm is placed on the top just to cover the cylinder that means its radius is 6 cm also. Therefore, Radius of hemisphere (R) = 6 cm

Radius of cylinder (r) = 6 cm

and height of cylinder (h) = 30 cm

Therefore, Volume of the solid = Volume of cylinder + Volume of hemisphere

= \( \Large \pi r^{2}h + \frac{2}{3} \pi R^{3} \)

= \( \Large \pi \left(6\right)^{2} \times 30 + \frac{2}{3} \pi \left(6\right)^{3} \)

= \( \Large \pi \times 36 \times 30 + \frac{2}{3} \pi \times 216 \)

= \( \Large 1080 \pi + 2 \pi \times 72 \)

= \( \Large 1080 \pi + 144 \pi \)

= \( \Large 1224 \pi cm^{3} \)

which is the required volume of solid.

Part of solved Volume and surface area questions and answers : >> Elementary Mathematics >> Volume and surface area

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