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A solid is in the shape of a cone standing on a hemisphere wit

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A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $1 c m$ and the height of the cone is equal to its radius. Find the volume of the solid in terms of $π$ .

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James Discussed

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to

1 c m

and the height of the cone is equal to its radius. Find the volume of the solid in terms of

π

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

Given:
Height (

h

) of conical part = radius (

r

) of conical part

= 1

cm
Radius (

r

) of hemispherical part = radius of conical part

= 1

cm
Volume of solid = Volume of conical part + Volume of hemispherical part

= \frac{1}{3} π r^{2} h + \frac{2}{3} π r^{3}

= \frac{1}{3} π \times 1^{2} \times 1 + \frac{2}{3} π \times 1^{3}

= \frac{1}{3} π \times 1 + \frac{2}{3} π \times 1

= \frac{π}{3} + \frac{2 π}{3} = π

^{3}

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Question Text	A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $1 c m$ and the height of the cone is equal to its radius. Find the volume of the solid in terms of $π$ .
Answer Type	Text solution:1
Upvotes	151