A gift box in the shape of a cylinder has a diameter of 8 in and height of 12 in which measurement is closest to the total surface area of the gift box in square inches
To find the total surface area of the gift box, we need to calculate the area of the two circular bases and the area of the curved side surface.
The area of each circular base can be found using the formula for the area of a circle: A = πr^2. We are given the diameter, so we'll start by dividing it by 2 to find the radius:
Radius = 8 in / 2 = 4 in
Area of each circular base = π(4 in)^2
= 16π in^2
The curved side surface of the cylinder is essentially a rectangle that has been rolled to form the cylinder. The length of the rectangle is equal to the perimeter of the circular base (since the base was rolled). The perimeter of a circle can be found using the formula: P = 2πr.
Perimeter of the circular base = 2π(4 in)
= 8π in
The height of the cylinder is the same as the width of the rectangle. Therefore, the area of the curved side surface is:
Area of the curved side surface = height × perimeter of the circular base
= 12 in × 8π in
= 96π in^2
Total surface area = 2 × Area of circular base + Area of curved side surface
= 2(16π in^2) + 96π in^2
= 32π in^2 + 96π in^2
= 128π in^2
To find the approximate value of the surface area, we can use the approximation π ≈ 3.14:
Total surface area ≈ 128 × 3.14 in^2
≈ 401.92 in^2
Therefore, the measurement closest to the total surface area of the gift box is 402 square inches.