# 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 #18 # and the height of the cylinder is #1 #. If the volume of the solid is #21 pi#, what is the area of the base of the cylinder?

The cylinder's height multiplied by the area of its circular base yields the volume of the cylinder.

A cone's volume can be calculated by multiplying the area of its circular base by one-third of its height.

The total volume of the solid is

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The area of the base of the cylinder is ( \frac{21\pi}{18} - \frac{1}{3} \times \pi \times 18^2 ). This simplifies to ( \frac{21\pi}{18} - \frac{1}{3} \times \pi \times 324 ), which equals ( \frac{7}{6}\pi - 108\pi ). This further simplifies to ( -\frac{641}{6}\pi ). Thus, the area of the base of the cylinder is ( \frac{641}{6}\pi ) square units.

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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.

- A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #6 #, its base's sides have lengths of #4 #, and its base has a corner with an angle of #( pi)/4 #. What is the pyramid's surface area?
- Two corners of an isosceles triangle are at #(2 ,4 )# and #(8 ,5 )#. If the triangle's area is #9 #, what are the lengths of the triangle's sides?
- What is the area of an equilateral triangle if you're given the length of one side?
- A cone has a height of #18 cm# and its base has a radius of #7 cm#. If the cone is horizontally cut into two segments #8 cm# from the base, what would the surface area of the bottom segment be?
- A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #7 #, its base has sides of length #6 #, and its base has a corner with an angle of #(3 pi)/4 #. What is the pyramid's surface area?

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