Question
The cone shown has a diameter of 12 centimeters and a slant height of 8 centimeters. Which choice is closest to the total surface area? Use 3.14 to approximate pi.
A. 151 square centimeters
B. 264 square centimeters
C. 301 square centimeters
D. 754 square centimeters
A. 151 square centimeters
B. 264 square centimeters
C. 301 square centimeters
D. 754 square centimeters
Answers
GPT 3.5
First, calculate the radius of the cone:
Radius = Diameter/2 = 12 cm / 2 = 6 cm
Now, use the slant height and radius to calculate the lateral surface area of the cone:
Lateral Surface Area = π * radius * slant height
Lateral Surface Area = 3.14 * 6 cm * 8 cm
Lateral Surface Area = 150.72 square centimeters
Next, calculate the base area of the cone:
Base Area = π * radius^2
Base Area = 3.14 * (6 cm)^2
Base Area = 3.14 * 36 cm^2
Base Area = 113.04 square centimeters
Total Surface Area = Lateral Surface Area + Base Area
Total Surface Area = 150.72 square centimeters + 113.04 square centimeters
Total Surface Area = 263.76 square centimeters
Therefore, the option closest to the total surface area is B. 264 square centimeters.
Radius = Diameter/2 = 12 cm / 2 = 6 cm
Now, use the slant height and radius to calculate the lateral surface area of the cone:
Lateral Surface Area = π * radius * slant height
Lateral Surface Area = 3.14 * 6 cm * 8 cm
Lateral Surface Area = 150.72 square centimeters
Next, calculate the base area of the cone:
Base Area = π * radius^2
Base Area = 3.14 * (6 cm)^2
Base Area = 3.14 * 36 cm^2
Base Area = 113.04 square centimeters
Total Surface Area = Lateral Surface Area + Base Area
Total Surface Area = 150.72 square centimeters + 113.04 square centimeters
Total Surface Area = 263.76 square centimeters
Therefore, the option closest to the total surface area is B. 264 square centimeters.