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A solid wooden toy is in the form of a cone mounted on a hemisphere. If the radii of hemisphere and base of cone are $4.2 cm$ each and the total height of toy is $10.2 cm$ , find the volume of wood used in the toy.

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266.112 c m 3

326.112 c m 3

375.458 c m 3

487.4 c m 3

answer is A.

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Detailed Solution

Given that, toy is made of hemisphere and cone, radius of hemisphere and cone is 4.2cm, height of toy is 10.2cm.
Volume of a cone

= 13 r 2 h

Here, r is radius, h is height.
Volume of a hemisphere

= 23 π r 3

Here, r is radius.
Volume of the toy = Volume of the hemispherical part + Volume of conical part
Height of the conical part,

10.2 − 4.2 = 6 cm

The volume of the solid,

⇒ 23 × 227 × 4.2 3 + 13 × 227 × 4.2 2 × 6 ⇒ 2221 × 4.2 2 × 8.4 + 6 ⇒ 266.112 c m 3

Thus, the required volume of the solid is

266.112 c m 3

.
Therefore, option (1) is correct.

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