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Question
The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown. Calculate: the total volume of the solid.
Solution
Diameter = 10 cm
Therefore, radius (r) = 5 cm
Height of the cone (h) = 12 cm
Height of the cylinder = 12 cm
`= 1/3 pi "r"^2"h" + pi"r"^2"h" + 2/3 pi "r"^3`
`= pi "r"^2 [1/3 "h" + "h" + 2/3 "r"]`
`= 22/7 xx 5 xx 5[1/3 xx 12 + 12 + 2/3 xx 5]`
`= 550/7 [4 + 12 + 10/3]`
`= 550/7 [16 + 10/3]`
`= 550/7 xx 58/3`
`= 31900/21`
= 1519.0476 cm3
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