We are given that the two following figures have the same volume.
We want to find the height of the cone. To do so, we will find an expression for the volume of each figure. Let's start with the cylinder. Recall that the volume of a cylinder with the radius r and height h can be calculated by the following formula.
V=π r^2 hIn this case, the radius is 5 centimeters and the height is 12 centimeters. We can substitute the height and the radius into the formula.
Volume of the cylinder=π * 5^2 * 12
Next, we will write the expression for the volume of the cone. To do so, let's recall that the volume of a cone with the radius r and height h can be calculated by the following formula.
V=1/3π r^2 h
This time, the radius is 5 centimeters and the height is x centimeters.
Volume of the cone=1/3* π * 5^2 * x
Using the fact that both figures have the same volume, we can write an equation that will help us to find the height of the cone.
π * 5^2 * 12 =1/3* π * 5^2* x
Now we can solve the equation for x.
