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 $66$ $66$ and the height of the cylinder is $5$ $5$ . If the volume of the solid is $45 π$ $45 pi$ , 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 $66$ $66$ and the height of the cylinder is $5$ $5$ . If the volume of the solid is $45 π$ $45 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2017-06-07T07:38:57

$\frac{5}{3} π$ $5/3 pi$

Explanation:

Let the 'radius' be r unit.
We know the volume of a cone = $\frac{1}{3} π r^{2} h_{1}$ $1/3 pi r^2 h_1$ cu. units [ $h_{1}$ $h_1$ is height which = 66.]

& volume of a cylinder = $π r^{2} h_{2}$ $pi r^2 h_2$ cu. units. [ $h_{2}$ $h_2$ is height which equals to 5]

As per questions, $\frac{1}{3} π r^{2} h_{1} + π r^{2} h_{2} = 45 π$ $1/3 pi r^2 h_1 + pi r^2 h_2 = 45 pi$

$\Rightarrow π r^{2} [\frac{1}{3} \cdot 66 + 5] = 45 π$ $rArr pi r^2[1/3* 66 + 5] = 45 pi$

$\Rightarrow r^{2} \cdot 27 = 45$ $rArr r^2*27 = 45$

$\Rightarrow r^{2} = \frac{45}{27}$ $rArr r^2 = 45/27$

Now area of the base of the cylinder = $π \cdot r^{2} = π \cdot \frac{45}{27} = \frac{5}{3} π$ $pi*r^2 = pi*45/27= 5/3 pi$

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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 $66$ $66$ and the height of the cylinder is $5$ $5$ . If the volume of the solid is $45 π$ $45 pi$ , 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 6666 and the height of the cylinder is 55 . If the volume of the solid is 45π45 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 $66$ $66$ and the height of the cylinder is $5$ $5$ . If the volume of the solid is $45 π$ $45 pi$ , what is the area of the base of the cylinder?