Question
7. \( \begin{aligned} V & =2912 \text { in. }^{3}, \ell=32 \text { in. }, \\ w & =13 \text { in. }, h=? ~ i n . ~\end{aligned} \)
Ask by Gonzalez Mcdonald. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The height is 7 inches.
Solution
The volume of a rectangular prism is given by the formula:
Volume = length × width × height
We are provided with:
Volume, V = 2912 in³
Length, ℓ = 32 in
Width, w = 13 in
To find the height, h, substitute the known values into the formula and solve for h:
2912 in³ = 32 in × 13 in × h
First, calculate the product of the length and width:
32 in × 13 in = 416 in²
Now, solve for h:
h = 2912 in³ ÷ 416 in²
h = 7 in
Thus, the height is 7 inches.
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Simplify this solution The Deep Dive
To find the height \( h \) of the rectangular prism, you can use the formula for the volume of a rectangular prism, which is given by: \[ V = \ell \times w \times h \] Substituting the known values into the formula, we have: \[ 2912 = 32 \times 13 \times h \] First, calculate \( 32 \times 13 \): \[ 32 \times 13 = 416 \] So the equation simplifies to: \[ 2912 = 416 \times h \] To solve for \( h \), divide both sides by 416: \[ h = \frac{2912}{416} = 7 \text{ in.} \] Thus, the height \( h \) is \( 7 \text{ in.} \).
