A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $42$ $42$ and the height of the cylinder is $1$ $1$ . If the volume of the solid is $495 π$ $495 pi$ , what is the area of the base of the cylinder?

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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $42$ $42$ and the height of the cylinder is $1$ $1$ . If the volume of the solid is $495 π$ $495 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2017-01-22T17:05:27

$33 π$ $33pi$ .

Explanation:

Let $r$ $r$ be the radius of the Cone, so, that of the Cylinder is also $r$ $r$ .

$Now, the Volume v_1 of the cone= \frac{1}{3} π r^{2} (height) = \frac{1}{3} π r^{2} (42)$ $"Now, the Volume v_1 of the cone="1/3pir^2"(height)"=1/3pir^2(42)$ ,

and, the Vvolume $v_{2} of the cylinder= π r^{2} (height) = π r^{2} (1) .$ $v_2" of the cylinder="pir^2"(height)"=pir^2(1).$

$:." Total Volume of the solid="v_1+v_2=14pir^2+pir^2=15pir^2$

As this Volume is $495pi," we have, "15pir^2=495pi$

$:."The Area of the base of the cylinder="pir^2=(495pi)/15=33pi$ .

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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $42$ $42$ and the height of the cylinder is $1$ $1$ . If the volume of the solid is $495 π$ $495 pi$ , what is the area of the base of the cylinder?

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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is 42 4242 and the height of the cylinder is 1 11 . If the volume of the solid is 495 pi495π495 pi, what is the area of the base of the cylinder?

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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $42$ $42$ and the height of the cylinder is $1$ $1$ . If the volume of the solid is $495 π$ $495 pi$ , what is the area of the base of the cylinder?