A cylinder is surmounted by a cone at one end a hemisphere at the other end The common radius is 3 5...........

Quantitative Aptitude ( CCS) Mensuration 3D

A cylinder is surmounted by a cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of the cylinder is 6.5 cm and the total height of the structure is 12.8 cm. The volume V of the structure lies between

370 cm² and 380 cm²

380 cm² and 390 cm²

390 cm² and 400 cm²

None of these

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Explanation:

Given that, Total height of the structure (H) = 12.8 cm and height of cylinder (h₁) = 6.5 cm
Common radius (r) = 3.5 cm
∴ height of hemisphere (h₂) = radius = 3.5 cm
and height of cone (h₃) = H – h₁ – h₂ = 12.8 – 6.5 – 3.5 = 2.8 cm
Now, Volume of the structure = Volume of cylinder + Volume hemisphere + Volume of cone