Question
Clayton wants to make a cylindrical case that will fit a bass drum with a height of 14 in. and a diameter of 24 in. What is the surface area of the case? Use 3.14 for π. Round to the nearest tenth.
Answers
GPT 3.5
To find the surface area of the cylindrical case, we first need to find the lateral surface area of the cylinder and then add the surface area of the two circular ends.
Lateral surface area = circumference of the base x height
Lateral surface area = 2πr x h
Lateral surface area = 2 x 3.14 x 12 x 14
Lateral surface area = 878.88 in²
Surface area of the circular ends = 2πr²
Surface area of the circular ends = 2 x 3.14 x 12²
Surface area of the circular ends = 904.32 in²
Total surface area = Lateral surface area + Surface area of the circular ends
Total surface area = 878.88 + 904.32
Total surface area = 1783.2 in²
Therefore, the surface area of the cylindrical case is approximately 1783.2 square inches.
Lateral surface area = circumference of the base x height
Lateral surface area = 2πr x h
Lateral surface area = 2 x 3.14 x 12 x 14
Lateral surface area = 878.88 in²
Surface area of the circular ends = 2πr²
Surface area of the circular ends = 2 x 3.14 x 12²
Surface area of the circular ends = 904.32 in²
Total surface area = Lateral surface area + Surface area of the circular ends
Total surface area = 878.88 + 904.32
Total surface area = 1783.2 in²
Therefore, the surface area of the cylindrical case is approximately 1783.2 square inches.