Use the image to answer the question.

Question

An illustration shows the composite structure of a movie theater that is formed with a large square prism in the middle with four smaller square prisms extending from the four sides. The entire structure is 20 meters in height. The square prism in the center measures 44 meters on each side. The smaller square prisms extend outward from the center of each side. The smaller square prisms are 15 meters on each side. A sign labeled Movies sits on the top of the structure.

What is the volume of the movie theater?

(1 point)
m3

Answer 1

To find the volume of the movie theater, find the volume of the large square prism in the middle and then the volume of the four smaller square prisms and add them together.

Volume of large square prism:
V = l^2 * h
V = 44^2 * 20
V = 968 * 20
V = 19360 m^3

Volume of one small square prism:
V = l^2 * h
V = 15^2 * 20
V = 225 * 20
V = 4500 m^3

Since there are four small square prisms, multiply the volume of one small square prism by 4:
4 * 4500 = 18000 m^3

Now, add the volumes together:
19360 + 18000 = 37360 m^3

So, the volume of the movie theater is 37360 m^3.

Answer 2

56,720