Apply the technique of using nets to find the surface area of a turtle’s tank, which measures 33.93 inches long by 15.81 inches wide by 17.69 inches tall. What is the surface area of the tank if the tank does not include a top cover? Round the answer to the nearest hundredth.

Question

Responses

2,296.23 in2
2,296.23 in squared

9,489.51 in2
9,489.51 in squared

1,416.33 in2
1,416.33 in squared

2,832.67 in2

Answer 1

To find the surface area of the tank without the top cover, we must first find the surface area of each of the six faces of the tank.

1. Front and back faces:
- Each front and back face has a length of 33.93 inches and a height of 17.69 inches.
- The surface area of each front and back face is 33.93 in * 17.69 in = 600.0617 in2.
- Since there are two front and back faces, the total surface area for both is 2 * 600.0617 in2 = 1,200.1234 in2.

2. Top and bottom faces:
- Each top and bottom face has a length of 33.93 inches and a width of 15.81 inches.
- The surface area of each top and bottom face is 33.93 in * 15.81 in = 535.1433 in2.
- Since there are two top and bottom faces, the total surface area for both is 2 * 535.1433 in2 = 1,070.2866 in2.

3. Side faces:
- Each side face has a width of 15.81 inches and a height of 17.69 inches.
- The surface area of each side face is 15.81 in * 17.69 in = 280.1889 in2.
- Since there are four side faces, the total surface area for all four is 4 * 280.1889 in2 = 1,120.7556 in2.

Adding up the surface area of all six faces, we get:
1,200.1234 in2 (front and back) + 1,070.2866 in2 (top and bottom) + 1,120.7556 in2 (side) = 3,391.1656 in2.

Therefore, the surface area of the turtle's tank without the top cover is 3,391.1656 square inches. Rounded to the nearest hundredth, the answer would be 3,391.17 in2.

So, none of the provided responses are correct.