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प्रश्न
A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.
उत्तर
We have,
Radius of cone = radius of hemisphere =r = 3.5 cm or AD = BD = CI
Total height of the solid, OC = 9.5 cm
`rArr OD + CD = 9.5`
`rArr OD + 3.5 = 9.5`
`rArr OD = 6 cm`
⇒ Height of cone, h = 6 cm
Now,
Volume of solid = Volume of cone + Volume of hemisphere
`= 1/3pir^2h + 2/3pir^3`
`=1/3 pir^2 (h + 2r)`
`=1/3xx22/7xx3.5xx3.5xx(6+2xx3.5)`
`= 1/3xx 22/7xx3.5xx3.5xx(6+7)`
`= 1/3xx22/7xx3.5xx3.5xx13`
`= 500.5/3`
≈ 166.83 cm3
So, the volume of the solid is 166.83 cm3.
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