# 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 #39 # and the height of the cylinder is #17 #. If the volume of the solid is #150 pi#, what is the area of the base of the cylinder?

The area of the base of the cylinder is

The following is the formula for the area of a circle's (or cylinder's) base:

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To find the area of the base of the cylinder, we first need to determine the radius of the cylinder. Since the radius of the cone is equal to that of the cylinder, we can use the height and volume information provided to find the radius of the cone.

The volume ( V ) of a cone is given by the formula:

[ V = \frac{1}{3}\pi r^2 h ]

Given that the volume of the solid is ( 150\pi ), and the height of the cone is ( 39 ), we can set up the equation:

[ 150\pi = \frac{1}{3}\pi r^2 \times 39 ]

Solving for ( r ):

[ r^2 = \frac{150\pi \times 3}{39\pi} ]

[ r^2 = \frac{450}{39} ]

[ r^2 = \frac{150}{13} ]

[ r = \sqrt{\frac{150}{13}} ]

Now, since the radius of the cylinder is the same as the radius of the cone, the radius of the cylinder is also ( \sqrt{\frac{150}{13}} ).

Finally, we can find the area of the base of the cylinder using the formula for the area ( A ) of a circle:

[ A = \pi r^2 ]

Substituting the value of ( r ):

[ A = \pi \left(\sqrt{\frac{150}{13}}\right)^2 ]

[ A = \pi \times \frac{150}{13} ]

[ A = \frac{150\pi}{13} ]

Therefore, the area of the base of the cylinder is ( \frac{150\pi}{13} ).

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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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