Question
The volume \( V \) enclosed by a rectangular solid with length \( I \), width \( w \), and height \( h \) is \( V=l \cdot w \cdot h \). Find \( V \) if: \( I=42 \) yards, \( w=\frac{5}{2} \) yards, and \( h=\frac{8}{3} \) yards The volume is \( \square \) cubic yards.
Ask by Colon Carroll. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The volume \( V \) is 280 cubic yards.
Solution
To find the volume V of the rectangular solid, use the formula:
V = length × width × height
Substitute the given values:
V = 42 yards × (5/2) yards × (8/3) yards
First, multiply the numbers:
Multiply numerators: 42 × 5 × 8 = 1680
Multiply denominators: 1 × 2 × 3 = 6
So, V = 1680 / 6
Divide:
1680 ÷ 6 = 280
Thus, the volume is 280 cubic yards.
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Simplify this solution The Deep Dive
To find the volume \( V \) of the rectangular solid, we simply need to plug in the given dimensions into the formula \( V = l \cdot w \cdot h \). Given: - \( l = 42 \) yards - \( w = \frac{5}{2} \) yards - \( h = \frac{8}{3} \) yards Now, we calculate: \[ V = 42 \cdot \frac{5}{2} \cdot \frac{8}{3} \] First, calculate \( \frac{5}{2} \cdot \frac{8}{3} \): \[ \frac{5 \cdot 8}{2 \cdot 3} = \frac{40}{6} = \frac{20}{3} \] Now, multiply this by \( 42 \): \[ V = 42 \cdot \frac{20}{3} = \frac{840}{3} = 280 \] Thus, the volume \( V \) is \( 280 \) cubic yards.
