The volume of the prism is 1122 cubic inches. use the formula V = BH to find the h of the prism. B= 93.5in.
The Correct Answer and Explanation is:
To find the height ( h ) of the prism, we will use the volume formula for a prism:
[
V = B \times h
]
where:
- ( V ) is the volume of the prism,
- ( B ) is the area of the base of the prism,
- ( h ) is the height of the prism.
Given:
- Volume ( V = 1122 ) cubic inches,
- Base area ( B = 93.5 ) square inches.
We need to solve for ( h ), the height of the prism. To do this, we can rearrange the formula to solve for ( h ):
[
h = \frac{V}{B}
]
Substitute the known values for ( V ) and ( B ):
[
h = \frac{1122}{93.5}
]
Now, perform the division:
[
h = 12 \text{ inches}
]
Conclusion:
The height ( h ) of the prism is 12 inches.
Explanation:
In this problem, we are given the volume and the base area of a prism. The formula for the volume of a prism is ( V = B \times h ), where ( V ) is the volume, ( B ) is the area of the base, and ( h ) is the height. This formula shows that the volume of a prism is the product of its base area and its height.
To find the height, we can rearrange the formula to solve for ( h ) by dividing both sides of the equation by ( B ), as follows:
[
h = \frac{V}{B}
]
Once we substitute the given values for ( V ) (1122 cubic inches) and ( B ) (93.5 square inches), we can calculate ( h ) by performing the division. The result is 12 inches, which means the height of the prism is 12 inches.
This approach is based on the relationship between the volume, base area, and height of a prism. By using the formula and rearranging it as needed, we can easily solve for any unknown variable if the others are provided.