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A solid is a cone mounted on a right circular cylinder with the same radius of their bases. The cone's base is placed on top of the cylinder's base. If the radius of the base and the height of the cone are 4 and 7, respectively, and the height of the cylindrical part of the solid is 3.5, The volume of the solid is equal to

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$293 \frac{1}{3} {cm}^{3}$

$293 \frac{1}{5} {cm}^{3}$

$298 \frac{1}{3} {cm}^{3}$

$298 \frac{1}{5} {cm}^{3}$

answer is A.

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Detailed Solution

Volume of the solid = Volume of the cylindrical part + Volume of conical

part

Volume of a Cylinder of Radius R and height $h = π R^{2} h$

Volume of a cone $= \frac{1}{3} π r^{2} h$ where r is radius and h is height of the cone.

Hence, Volume of the solid $= \frac{22}{7} \times 4 \times 4 \times 3.5 + \frac{1}{3} \times \frac{22}{7} \times 4^{2} \times 7$

$= 176 + \frac{352}{3}$

$= 293 \frac{1}{3} {cm}^{2}$

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