Question

a composite figure is shown. the surface area is 924π square units. the height of the cylinder is four times the height of the cone. what are the heights of the cone and the cylinder? the height of the cone is units. the height of the cylinder is units.

Explanation:

Step1: Identify given - height relationship

The height of the cylinder is four times the height of the cone. Let the height of the cone be $h_{cone}$ and the height of the cylinder be $h_{cylinder}$. So $h_{cylinder}=4h_{cone}$.

Step2: Use the given values from the figure

From the figure, we can see that the height of the cone is 12 units.

Step3: Calculate the height of the cylinder

Since $h_{cylinder}=4h_{cone}$ and $h_{cone} = 12$ units, then $h_{cylinder}=4\times12 = 48$ units.

Answer:

The height of the cone is 12 units. The height of the cylinder is 48 units.