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The radius of the hemisphere and the cone-shaped solid are both equal to one centimetre, and the height of the cone is proportional to its radius. Determine the solid's volume. Use $π = 227$ .

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π 2 c m 3

π c m 3

2 π c m 3

3 π c m 3

answer is B.

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Detailed Solution

Given that
Height of the cone

= h = 10 c m

and Radius of cone,

r = 3.5 c m

Radius of hemisphere,

r = 1 c m

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its

Total volume of the solid = Volume of cone +Volume of hemisphere
Volume of cone

= 13 π r 2 h

R a d i u s = r = 1 c m H e i g h t = h = 1 c m

⇒ V o l u m e = 13 π × (1) 2 × 1 ⇒ V o l u m e = 13 π c m 3

Volume of hemisphere

= 23 π r 3

R a d i u s = r = 1 c m

⇒ V o l u m e = 23 π (1) 3 ⇒ V o l u m e = 23 π c m 3

Total volume of the solid = Volume of cone + Volume of hemisphere

⇒ T o t a l v o l u m e = 13 π + 23 π

⇒ T o t a l v o l u m e = 33 π ⇒ T o t a l v o l u m e = π c m 3

Hence, total volume of the solid

= π c m 3

Therefore the answer is option (2).

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