Question
6. \( \begin{aligned} V & =2304 \mathrm{~cm}^{3}, l=32 \mathrm{c} \\ w & =? \mathrm{~cm}, h=8 \mathrm{~cm}\end{aligned} \)
Ask by Huff Garrett. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The width is 9 cm.
Solution
We are given the volume formula for a rectangular prism:
Volume (V) = length (l) × width (w) × height (h)
We know:
V = 2304 cm³
l = 32 cm
h = 8 cm
To find the width (w), rearrange the formula:
w = V / (l × h)
Substitute the given values:
w = 2304 cm³ / (32 cm × 8 cm)
w = 2304 cm³ / 256 cm²
w = 9 cm
Thus, the width is 9 cm.
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Simplify this solution Extra Insights
To find the width \( w \) of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is \( V = l \times w \times h \). Given: - Volume \( V = 2304 \, \text{cm}^3 \) - Length \( l = 32 \, \text{cm} \) - Height \( h = 8 \, \text{cm} \) We can rearrange the formula to solve for \( w \): \[ w = \frac{V}{l \times h} \] Now plug in the values: \[ w = \frac{2304 \, \text{cm}^3}{32 \, \text{cm} \times 8 \, \text{cm}} = \frac{2304}{256} = 9 \, \text{cm} \] Thus, the width \( w \) is \( 9 \, \text{cm} \).
