College

A box is in the shape of a square prism. The height of the box is 9 inches, and the area of the square base is 16 square inches.

What is the total surface area in square inches of the box?

A. 176 square inches
B. 226 square inches
C. 144 square inches
D. 244 square inches

Answer :

Final answer:

The total surface area of the square prism (box) is 176 square inches, calculated by adding the area of the two square bases and the lateral faces together.

Explanation:

To find the total surface area of the square prism (which is also known as a box), we need to calculate the area of all of its faces. Since the base of the box is a square with an area of 16 square inches, each side of the square base is 4 inches (since 4 inches x 4 inches = 16 square inches). The box has two bases (top and bottom) and four lateral faces. The height of the box is 9 inches.

  1. Calculate the area of the two bases: 16 square inches (base area) x 2 (top and bottom) = 32 square inches.
  2. Calculate the area of one of the lateral faces: 9 inches (height) x 4 inches (side of the base) = 36 square inches. Since there are four lateral faces, multiply by 4 to get the total lateral surface area: 36 square inches x 4 faces = 144 square inches.
  3. Finally, add the area of the bases to the lateral surface area to find the total surface area: 32 square inches (bases) + 144 square inches (lateral faces) = 176 square inches.

Therefore, the total surface area of the box is 176 square inches.