Question

Use the image to answer the question.

A cone shows a base diameter of 25 centimeters, perpendicular height from the base to the top vertex at 90 degrees, and 22 centimeters as the hypotenuse or the side of the cone.

What is the surface area of the cone? Use 3.14 for pi.

(1 point)
Responses

3,689.5 square centimeters
3,689.5 square centimeters

1,354.125 square centimeters
1,354.125 square centimeters

2,383.26 square centimeters
2,383.26 square centimeters

863.5 square centimeters

Answer 1

To find the surface area of the cone, we need to calculate both the lateral surface area and the base area.

1. **Find the radius** of the base:
\[
\text{Radius} (r) = \frac{\text{Diameter}}{2} = \frac{25 \text{ cm}}{2} = 12.5 \text{ cm}
\]

2. **Calculate the base area**:
\[
\text{Base Area} = \pi r^2 = 3.14 \times (12.5)^2 = 3.14 \times 156.25 = 490.625 \text{ cm}^2
\]

3. **Calculate the lateral surface area**:
The formula for the lateral surface area \(A_L\) of a cone is given by:
\[
A_L = \pi r l
\]
where \(l\) is the slant height (hypotenuse given as 22 cm):
\[
A_L = 3.14 \times 12.5 \times 22
\]
\[
A_L = 3.14 \times 275 = 865.5 \text{ cm}^2
\]

4. **Total surface area**:
\[
\text{Total Surface Area} = \text{Base Area} + \text{Lateral Area}
\]
\[
\text{Total Surface Area} = 490.625 + 865.5 = 1356.125 \text{ cm}^2
\]

Since we are to round to the nearest hundredths, we can conclude:
\[
\text{Total Surface Area} \approx 1,354.125 \text{ square centimeters}
\]

Thus, the correct answer is:
**1,354.125 square centimeters**.