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?
a 402.12 in.^2
b 301.59 in.^2
c 1,005.31 in.^2
d 603.19 in.^2
To find the total surface area of the gift box, we need to calculate the surface area of the curved part (lateral surface area) and the surface areas of the two circular bases.
The lateral surface area of a cylinder can be found using the formula:
Lateral Surface Area = 2πrh
where r is the radius and h is the height.
In this case, the diameter is given as 8 inches, so the radius is half of that, which is 4 inches.
The height is given as 12 inches.
Lateral Surface Area = 2π(4)(12) = 96π
The surface area of a circle can be found using the formula:
Surface Area of a Circle = πr²
where r is the radius.
In this case, the radius is 4 inches.
Surface Area of a Circle (each base) = π(4)² = 16π
To find the total surface area, we need to add the lateral surface area to the surface areas of the two bases.
Total Surface Area = Lateral Surface Area + 2 × Surface Area of a Circle
Total Surface Area = 96π + 2(16π) = 96π + 32π = 128π
To find the answer in square inches, we need to approximate the value of π to the nearest hundredth. π is often approximated as 3.14.
Total Surface Area ≈ 128(3.14) = 401.92
From the given options, the measurement closest to the total surface area is 402.12 in².
Therefore, the closest measurement to the total surface area of the gift box is 402.12 in².