To find the volume of the movie theater, we need to find the volume of the large square prism in the center and the four smaller square prisms extending from the sides.
The volume of a square prism is given by the formula V = l^2 * h, where l is the side length of the base and h is the height.
For the large square prism in the center:
V = 44^2 * 20
V = 19360 * 20
V = 387,200 cubic meters
For each of the four smaller square prisms:
V = 15^2 * 20
V = 225 * 20
V = 4,500 cubic meters
Therefore, the total volume of the movie theater is:
387,200 + 4 * 4,500 = 387,200 + 18,000 = 405,200 cubic meters
The volume of the movie theater is 405,200 cubic meters.
Use the image to answer the 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?
7 answers
is this correct?
I apologize for the error in my previous response. Let's correct that:
The volume of the large square prism in the center is:
V_center = 44^2 * 20 = 38,720 * 20 = 774,400 cubic meters
The volume of each of the four smaller square prisms is:
V_small = 15^2 * 20 = 225 * 20 = 4,500 cubic meters
Since there are four smaller square prisms, the total volume of the four is:
V_total_small = 4 * 4,500 = 18,000 cubic meters
Therefore, the total volume of the movie theater is the sum of the volume of the large square prism in the center and the four smaller square prisms:
Total Volume = V_center + V_total_small
Total Volume = 774,400 + 18,000
Total Volume = 792,400 cubic meters
The correct volume of the movie theater is 792,400 cubic meters. Thank you for pointing out the error.
The volume of the large square prism in the center is:
V_center = 44^2 * 20 = 38,720 * 20 = 774,400 cubic meters
The volume of each of the four smaller square prisms is:
V_small = 15^2 * 20 = 225 * 20 = 4,500 cubic meters
Since there are four smaller square prisms, the total volume of the four is:
V_total_small = 4 * 4,500 = 18,000 cubic meters
Therefore, the total volume of the movie theater is the sum of the volume of the large square prism in the center and the four smaller square prisms:
Total Volume = V_center + V_total_small
Total Volume = 774,400 + 18,000
Total Volume = 792,400 cubic meters
The correct volume of the movie theater is 792,400 cubic meters. Thank you for pointing out the error.
give me the equation needed to solve this all quickly just by searching it up
The formula needed to calculate the volume of a composite structure like the movie theater described in the image is the sum of the volumes of the individual components.
So, for this specific case, you would use the formula:
Total Volume = Volume of the large square prism in the center + (Number of smaller square prisms * Volume of each smaller square prism)
In this case:
Total Volume = (side length of the large square prism)^2 * height of the large square prism + (4 * (side length of each smaller square prism)^2 * height of each smaller square prism)
You can plug in the values of the side lengths and heights provided in the image into this formula to quickly calculate the total volume of the movie theater.
So, for this specific case, you would use the formula:
Total Volume = Volume of the large square prism in the center + (Number of smaller square prisms * Volume of each smaller square prism)
In this case:
Total Volume = (side length of the large square prism)^2 * height of the large square prism + (4 * (side length of each smaller square prism)^2 * height of each smaller square prism)
You can plug in the values of the side lengths and heights provided in the image into this formula to quickly calculate the total volume of the movie theater.
simplify the equation
The simplified equation for calculating the volume of the composite movie theater structure described in the image is:
Total Volume = (44^2 * 20) + (4 * (15^2 * 20))
You can directly substitute the values of the side lengths and heights into this simplified formula to find the total volume of the movie theater.
Total Volume = (44^2 * 20) + (4 * (15^2 * 20))
You can directly substitute the values of the side lengths and heights into this simplified formula to find the total volume of the movie theater.
1 answer