# 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 #27 # and the height of the cylinder is #7 #. If the volume of the solid is #42 pi#, what is the area of the base of the cylinder?

The area is

Total amount

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Given the volume of the solid and the dimensions of the cone and cylinder, you can set up an equation to find the radius of the cylinder and then use it to calculate the area of the base of the cylinder.

Let's denote:

- ( r ) as the radius of the cylinder (and also the radius of the cone)
- ( h_c ) as the height of the cone
- ( h_{\text{cy}} ) as the height of the cylinder

The volume of the solid is the sum of the volumes of the cone and the cylinder:

[ V_{\text{total}} = V_{\text{cone}} + V_{\text{cylinder}} ]

[ V_{\text{total}} = \frac{1}{3} \pi r^2 h_c + \pi r^2 h_{\text{cy}} ]

Given that ( h_c = 27 ) and ( h_{\text{cy}} = 7 ), and that ( V_{\text{total}} = 42\pi ), we can substitute these values into the equation to solve for ( r ).

[ 42\pi = \frac{1}{3} \pi r^2 \cdot 27 + \pi r^2 \cdot 7 ]

Solve for ( r ), then use it to find the area of the base of the cylinder using the formula:

[ A_{\text{cylinder base}} = \pi r^2 ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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