What is the surface area of the cone? Slant height:22 Radius:25
A. 2,383.26 square centimeters
B. 863.5 square centimeters
C. 3,689.5 square centimeters
D. 1,354.125 square centimeters
To calculate the surface area of a cone, you need to calculate the area of the circular base and the lateral surface area of the cone.
The area of the circular base is given by the formula:
\[ A_{base} = \pi r^2 \]
where \( r \) is the radius of the base.
Using the given radius \( r = 25 \) cm, the base area is:
\[ A_{base} = \pi \times 25^2 = \pi \times 625 \]
The lateral surface area of the cone is given by the formula:
\[ A_{lateral} = \pi r l \]
where \( l \) is the slant height of the cone.
Using the given slant height \( l = 22 \) cm, the lateral surface area is:
\[ A_{lateral} = \pi \times 25 \times 22 = \pi \times 550 \]
Adding the two areas together, the total surface area of the cone \( A_{total} \) is:
\[ A_{total} = A_{base} + A_{lateral} = \pi \times 625 + \pi \times 550 \]
\[ A_{total} = \pi \times (625 + 550) \]
\[ A_{total} = \pi \times 1175 \]
Using \( \pi \approx 3.14159 \), we get:
\[ A_{total} \approx 3.14159 \times 1175 \]
\[ A_{total} \approx 3690.81825 \]
The closest answer to the actual surface area in square centimeters, rounding to one decimal place, is:
C. 3,689.5 square centimeters