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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 for formed ?
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- 264π cm3
- 252π cm3
- 236π cm3
- None of these
- 264π cm3
Correct Option: D
If 10 circular plates each of thickness 3 cm, each are placed one above the other, then it forms a cylinder with height (3 x 10 = 30 cm) 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
∴ Radius of hemisphere (R) = 6 cm
Radius of cylinder (r) = 6 cm
and height of cylinder (h) = 30 cm
∴ Volume of the solid = Volume of cylinder + Volume of hemisphere
= πr2h + (2/3)πR3
= π(6)2 x 30 + (2/3)π(6)3
= π x 36 x 30 + (2/3)π x 216
= 1080π + 2π x 72 = 1080π + 144π
= 1224π cm3
Which is the required volume of solid.