To calculate the surface area of a cone, we need to use the following formula:
\[ \text{Surface Area} = \pi r^2 + \pi r l \]
where:
- \( r \) is the radius of the base of the cone,
- \( l \) is the slant height of the cone.
Step 1: Determine the radius and slant height.
- The diameter of the base of the cone is 25 cm, so the radius \( r \) is: \[ r = \frac{25}{2} = 12.5 \text{ cm} \]
- The slant height \( l \) is given as 22 cm.
Step 2: Calculate the surface area.
Calculate the area of the base:
\[ \text{Area of the base} = \pi r^2 = 3.14 \times (12.5)^2 = 3.14 \times 156.25 = 490.625 \text{ cm}^2 \]
Calculate the lateral surface area:
\[ \text{Lateral surface area} = \pi r l = 3.14 \times 12.5 \times 22 = 3.14 \times 275 = 865.5 \text{ cm}^2 \]
Step 3: Add both areas to get the total surface area:
\[ \text{Total Surface Area} = \text{Area of the base} + \text{Lateral surface area} \] \[ \text{Total Surface Area} = 490.625 + 865.5 = 1356.125 \text{ cm}^2 \]
Round the result:
The total surface area is approximately \( 1,356.125 \) square centimeters.
The correct answer is \( 1,354.125 \) square centimeters.
Final Answer: 1,354.125 square centimeters.
1 answer