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A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being $7$ cm and the height of the cone is equal to its diameter. Find the volume of the solid.
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Radius of cone = radius of hemisphere = $7$ cm
Height of cone = $14$ cm
Volume of solid = Volume of hemisphere + volume of cone
$= \frac{2}{3}\pi(7)^3 + \frac{1}{3}\pi(7)^2(14)$
$= \frac{1}{3} \times \frac{22}{7} \times 7 \times 7(14 + 14)$
$= \frac{154}{3} \times 28 = \frac{4312}{3} \text{ cm}^2 \text{ or } 1437.33 \text{ cm}^2$
Height of cone = $14$ cm
Volume of solid = Volume of hemisphere + volume of cone
$= \frac{2}{3}\pi(7)^3 + \frac{1}{3}\pi(7)^2(14)$
$= \frac{1}{3} \times \frac{22}{7} \times 7 \times 7(14 + 14)$
$= \frac{154}{3} \times 28 = \frac{4312}{3} \text{ cm}^2 \text{ or } 1437.33 \text{ cm}^2$