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
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.