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.2603
The total surface area of a cylinder can be calculated using the formula 2πr^2 + 2πrh, where r is the radius and h is the height.
In this case, the diameter of the cylinder is 8 inches, so the radius is 8/2 = 4 inches. The height is 12 inches.
Plugging these values into the formula, the total surface area is 2π(4^2) + 2π(4)(12) = 2π(16) + 2π(48) = 32π + 96π = 128π.
To find the closest measurement, we can use the approximation π ≈ 3.14. So, 128π ≈ 128(3.14) = 401.92.
The closest measurement to 401.92 is 402.12, so the answer is A) 402.12 in^2.