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 $24$ $24$ and the height of the cylinder is $4$ $4$ . If the volume of the solid is $90 π$ $90 pi$ , 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 $24$ $24$ and the height of the cylinder is $4$ $4$ . If the volume of the solid is $90 π$ $90 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2017-12-28T01:19:25

Base Area $= 23.56$ $= 23.56$

Explanation:

Combine the equations for the volumes of the cylinder and the cone to find the radius. Then calculate the base area ( $π r^{2}$ $pir^2$ ).

$V_{cone} = \frac{1}{3} π r^{2} h$ $V_"cone" = 1/3pir^2h$
$V_{cyl} = π r^{2} h$ $V_"cyl" = pir^2h$

$V = 90 π = \frac{1}{3} π r^{2} h + π r^{2} h$ $V = 90pi = 1/3pir^2h + pir^2h$

$90 = \frac{1}{3} r^{2} \times 24 + r^{2} \times 4 = 12 r^{2}$ $90 = 1/3r^2xx24 + r^2xx4 = 12r^2$
$r^{2} = 7.5$ $r^2 = 7.5$

Because we want $r^{2}$ $r^2$ for the area anyway, we do not need to go further.
Base Area = $π r^{2} = π \times 7.5 = 23.56$ $pir^2 = pixx7.5 = 23.56$

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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 $24$ $24$ and the height of the cylinder is $4$ $4$ . If the volume of the solid is $90 π$ $90 pi$ , what is the area of the base of the cylinder?

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Explanation:

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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 $24$ $24$ and the height of the cylinder is $4$ $4$ . If the volume of the solid is $90 π$ $90 pi$ , what is the area of the base of the cylinder?