The Correct Answer and Explanation is:
The problem asks to find the height h of a prism using the formula V = Bh, given that the volume V is 1122 cubic inches. To solve for the height, we need to algebraically rearrange the formula.
Correct Answer
The height h of the prism is given by the expression h = 1122 / B. A specific numerical value for the height cannot be calculated because the area of the base, B, is not provided in the problem statement.
Explanation
The problem provides the formula for the volume of a prism, V = Bh, where V represents the volume, B represents the area of the prism’s base, and h represents its height. We are given the volume V as 1122 cubic inches and are tasked with finding the height h.
To find the height, we must isolate the variable h in the equation. We can achieve this through a simple algebraic manipulation. Starting with the formula V = Bh, we can divide both sides of the equation by the base area B. This operation cancels B on the right side, leaving h by itself. The resulting formula is h = V / B.
Now, we can substitute the given value for the volume V into this new equation:
h = 1122 / B
This expression tells us that the height of the prism is equal to 1122 divided by the area of its base. However, the problem as presented in the image does not give the value of the base area B or provide the dimensions of the prism’s base (such as length and width for a rectangle, or base and height for a triangle). Without this crucial piece of information, we cannot perform the final division to find a specific numerical value for h.
For example, if the problem had specified that the base area B was 66 square inches, the calculation would be:
h = 1122 / 66 = 17 inches.
Therefore, the solution remains an expression dependent on the unknown base area B. To complete the problem, one would need to calculate or be given the value of B.
