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The adjoining figure shows a hemisphere of radius 5 cm surmounted by a right circular cone of base radius 5 cm. Find the volume of the solid if the height of the cone is 7 cm. Give your answer correct to two places of decimal.

The adjoining figure shows a hemisphere of radius 5 cm surmounted by a right circular cone of base radius 5 cm. Find the volume of the solid if the height of the cone is 7 cm. Give your answer correct to two places of decimal. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Mensuration

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Answer

Height of the conical part (h) = 7 cm.

Radius of base (r) = 5 cm.

The adjoining figure shows a hemisphere of radius 5 cm surmounted by a right circular cone of base radius 5 cm. Find the volume of the solid if the height of the cone is 7 cm. Give your answer correct to two places of decimal. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Volume of solid (V) = Volume of hemisphere + Volume of cone

V=23πr3+13πr2h=13πr2(2r+h)=13×227×52×(2×5+7)=2221×25×17=9350021=445.24 cm3.V = \dfrac{2}{3}πr^3 + \dfrac{1}{3}πr^2h \\[1em] = \dfrac{1}{3}πr^2(2r + h) \\[1em] = \dfrac{1}{3} \times \dfrac{22}{7} \times 5^2 \times (2 \times 5 + 7) \\[1em] = \dfrac{22}{21} \times 25 \times 17 \\[1em] = \dfrac{93500}{21} \\[1em] = 445.24 \text{ cm}^3.

Hence, the volume of the solid is 445.24 cm3.

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