A hemispherical bowl fits exactly on the flat surface of a right circular cone whose nbsp-height is 5 cm and radius is 3-5 cm- Find the volume of the solid formed- 144 cm3-132 cm3-154 cm3-169 cm3-

The correct option is C 154 cm3 We know that, volume of cone =1/3π r^2 h volume nbsp;of hemisphere nbsp;=2/3π r^3 Total volume nbsp; nbsp; = Volume ...

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Standard X

Mathematics

Volume of Combined Solids

A hemispheric...

Question

A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.

144 cm³

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132 cm³

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154 cm³

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169 cm³

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Solution

The correct option is C
154 cm³

We know that,
volume of cone $= \frac{1}{3} π r^{2} h$
volume of hemisphere $= \frac{2}{3} π r^{3}$

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

$= \frac{1}{3} π r^{2} h + \frac{2}{3} π r^{3} = \frac{1}{3} π r^{2} (h + 2 r) = \frac{1}{3} \times \frac{22}{7} \times {3.5}^{2} \times (5 + 7) = \frac{1}{3} \times \frac{22}{7} \times {3.5}^{2} \times 12 = 22 \times 0.5 \times 3.5 \times 4 = 154 {cm}^{3}$

$∴$ The volume of the solid formed is
$154 {cm}^{3}$

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A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.

The correct option is C 154 cm3 We know that, volume of cone =13πr2h volume of hemisphere =23πr3 Total volume = Volume of the cone + Volume of the hemisphere =13πr2h+23πr3=13πr2(h+2r)=13×227×3.52×(5+7)=13×227×3.52×12=22×0.5×3.5×4=154 cm3 ∴ The volume of the solid formed is 154 cm3