Question

A figure composed of a right cone and a right cylinder with dimensions in feet (ft) is shown.







What is the exact surface area, in square feet, of the figure

Answer 1

To calculate the exact surface area of a figure composed of a right cone and a right cylinder, we need the dimensions for both shapes, such as the radius and height.

### Surface Area of a Right Cone
The surface area \( A_{cone} \) of a right cone is given by the formula:

\[
A_{cone} = \pi r^2 + \pi r l
\]

Where:
- \( r \) is the radius of the base of the cone.
- \( l \) is the slant height of the cone. If you don't have the slant height, it can be found using the Pythagorean theorem:

\[
l = \sqrt{r^2 + h_{cone}^2}
\]

Where:
- \( h_{cone} \) is the height of the cone.

### Surface Area of a Right Cylinder
The surface area \( A_{cylinder} \) of a right cylinder is given by the formula:

\[
A_{cylinder} = 2\pi r^2 + 2\pi rh
\]
Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height of the cylinder.

### Total Surface Area Calculation
The total surface area \( A_{total} \) of the figure (assuming the base of the cone is on top of the cylinder) can be computed as:

\[
A_{total} = A_{cylinder} + A_{cone} - \text{(area of the base of the cone)}
\]

The area of the base of the cone is \( \pi r^2 \). Hence,

\[
A_{total} = A_{cylinder} + A_{cone} - \pi r^2
\]

### Final Steps
To find the exact surface area, you will need to provide the dimensions (radii and heights) of the cone and cylinder.
Once you have those:

1. Calculate the parameters \( A_{cone} \) and \( A_{cylinder} \).
2. Use the total surface area formula to get \( A_{total} \).

Please provide the dimensions of the cone and cylinder for a specific calculation.