A gift box in the shape of a cylinder has a diameter of 8 inches and a height of 12 inches. Which measurement is closest to the total surface area of the gift box in square inches?
Responses
A 402.12 in.2402.12 in. 2
B 301.59 in.2301.59 in. 2
C 1,005.31 in.21,005.31 in. 2
D 603.19 in.2
The total surface area of a cylinder can be found by adding the areas of the two circular bases and the lateral surface area.
The area of each circular base is equal to πr^2, where r is the radius. Since the diameter is 8 inches, the radius is 8/2 = 4 inches.
The area of each circular base is then π(4^2) = 16π square inches.
The lateral surface area of a cylinder can be found by multiplying the height of the cylinder by the circumference of the circular base. The circumference of a circle is given by 2πr, so in this case it is 2π(4) = 8π inches. Therefore, the lateral surface area is 8π(12) = 96π square inches.
Adding the areas of the two circular bases and the lateral surface area gives a total surface area of 16π + 16π + 96π = 128π square inches.
To find the closest measurement to the total surface area, we can use the approximation π ≈ 3.14.
128π ≈ 128(3.14) = 401.92
Therefore, the closest measurement to the total surface area of the gift box is 402.12 square inches.
The correct response is A, 402.12 in.2.