A hemispherical bowl fits exactly on the flat surface of a right circular cone w

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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. The volume of the solid formed is______.

Options:

A . 144 cm³

B . 132 cm³

C . 154 cm³

D . 169 cm³

Answer: Option C
:
C

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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