Question

find the missing length.
volume = 220.5 cm³
7 cm
7 cm
w
w = cm

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, \( l = 7 \) cm, \( h = 7 \) cm, and \( V = 220.5 \) \( \text{cm}^3 \).

Step2: Substitute the known values into the formula

Substitute \( l = 7 \), \( h = 7 \), and \( V = 220.5 \) into \( V = l \times w \times h \):
\( 220.5 = 7 \times w \times 7 \)
Simplify the right - hand side: \( 7\times7 = 49 \), so the equation becomes \( 220.5 = 49w \).

Step3: Solve for \( w \)

To find \( w \), divide both sides of the equation \( 220.5 = 49w \) by 49:
\( w=\frac{220.5}{49} \)
Calculate \( \frac{220.5}{49}=4.5 \).

Answer:

4.5