Question

find the missing length.
volume = 177,500 mm³
image of a cd case with dimensions 142 mm, 10 mm, and h
h = blank mm

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height. Here, \( l = 142 \) mm, \( w = 10 \) mm, and \( V = 177500 \) \( \text{mm}^3 \).

Step2: Rearrange the formula to solve for \( h \)

From \( V = l \times w \times h \), we can solve for \( h \) by dividing both sides by \( l \times w \). So, \( h=\frac{V}{l\times w} \).

Step3: Substitute the given values into the formula

Substitute \( V = 177500 \), \( l = 142 \), and \( w = 10 \) into the formula: \( h=\frac{177500}{142\times10} \).
First, calculate the denominator: \( 142\times10 = 1420 \).
Then, divide the numerator by the denominator: \( h=\frac{177500}{1420}=12.5 \).

Answer:

12.5