A solid consisting of right circular cylinder with a hemisphere of one end and a cone and the other. Their common radius is 7 cm. The height of cylinder and cone are each of 4 cm. Find the volume of the solid.

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Solution

REF.Image
Given,
height of cylinder = height of cone = $4 c m$
radius of all = $7 c m$
To find : volume of the figure
Th collective volume = volume of hemisphere + volume of cylinder + volume of cone
$\Rightarrow v o l u m e = (2 / 3 π r^{3} + π r^{2} h + \frac{1}{3} π r^{2} h) u n i t^{3}$
$= 2 / 3 π (7^{3}) + π (7^{2}) 4 + \frac{1}{3} π (7^{2}) 4 c m^{3}$
$= 49 π (14 / 3 + 4 + 4 / 3) c m^{3} = 49 π (\frac{14 + 12 + 4}{3})$
$= 490 π c m^{3}$
$= 490 \times 22 / 7 c m^{3} = 1540 c m^{3}$

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