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.
To find the surface area of the tank, we need to find the area of each side and then add them all together. We can use nets to help visualize the sides.
The net for the tank will have six sides: a bottom, a top (which we are assuming doesn't exist), a front, a back, and two sides. We can find the area of each side separately, and then add them up.
First, we'll find the area of the bottom. The bottom of the tank is a rectangle with a length of 33.93 inches and a width of 15.81 inches. Therefore, the area of the bottom is:
33.93 in. x 15.81 in. = 536.97 square inches
Next, we'll find the area of the front and back. Each of these sides is a rectangle with a height of 17.69 inches and a width of 15.81 inches. Therefore, the area of each side is:
15.81 in. x 17.69 in. = 279.73 square inches
Since there are two of these sides, we'll multiply by 2:
279.73 in.² x 2 = 559.46 square inches
Now, we'll find the area of the two sides. Each of these sides is a rectangle with a height of 17.69 inches and a length of 33.93 inches. Therefore, the area of each side is:
33.93 in. x 17.69 in. = 600.02 square inches
Since there are two of these sides, we'll multiply by 2:
600.02 in.² x 2 = 1200.04 square inches
Finally, we'll add up the area of all six sides to find the total surface area:
536.97 in.² + 559.46 in.² + 1200.04 in.² = 2296.47 in.²
Therefore, the surface area of the tank is approximately 2296.47 square inches. Rounded to the nearest hundredth, the answer is 2296.47 square inches.