Question
What is the volume of the prism?
A prism has hexagon bases with each side 12 centimeters. From the side of the base to the center of the base is 10 centimeters. The height of the prism is 9 centimeters.
1,080 cm3
2,700 cm3
3,240 cm3
6,480 cm3
A prism has hexagon bases with each side 12 centimeters. From the side of the base to the center of the base is 10 centimeters. The height of the prism is 9 centimeters.
1,080 cm3
2,700 cm3
3,240 cm3
6,480 cm3
Answers
GPT 3.5
The volume of a prism can be calculated by multiplying the area of the base by the height.
To find the area of the hexagon base, we can use the formula: A = (3/2) x (s^2) x √3, where s is the length of one side of the hexagon.
A = (3/2) x (12^2) x √3
A = (3/2) x 144 x √3
A = 216√3
Now, we can calculate the volume of the prism:
V = A x h
V = 216√3 x 9
V = 1944√3 cubic centimeters
Using a calculator to calculate √3 = 1.732
V = 1944 x 1.732
V ≈ 3367.008 cubic centimeters
Therefore, the volume of the prism is closest to 3,367 cubic centimeters.
In the provided options, the closest option is 3,240 cm3.
To find the area of the hexagon base, we can use the formula: A = (3/2) x (s^2) x √3, where s is the length of one side of the hexagon.
A = (3/2) x (12^2) x √3
A = (3/2) x 144 x √3
A = 216√3
Now, we can calculate the volume of the prism:
V = A x h
V = 216√3 x 9
V = 1944√3 cubic centimeters
Using a calculator to calculate √3 = 1.732
V = 1944 x 1.732
V ≈ 3367.008 cubic centimeters
Therefore, the volume of the prism is closest to 3,367 cubic centimeters.
In the provided options, the closest option is 3,240 cm3.