# 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 #33 # and the height of the cylinder is #13 #. If the volume of the solid is #256 pi#, what is the area of the base of the cylinder?

##### 2 Answers

#### Explanation:

A Conical Volume is given by:

A Cylindrical Volume is given by:

Circular Area (base of cylinder)

Total solid volume =

#### Explanation:

Let's consider the diagram

We need to find the area of the base of the cylinder, which is a circle. The area of a circle is given by

#color(blue)("Area of circle"=pir^2#

Where

The total volume of the solid is

Therefore,

#color(purple)("Volume of cone"+"Volume of cylinder"=256pi #

We use the formulas

#color(orange)("Volume of cone"=1/3pir^2#

#color(orange)("Volume of cylinder"=pir^2h#

Where,

Now, Let's find the area of the base