Question

find the missing length.
volume = 1620 cm³
image of a rectangular prism (vase) with length 9 cm, width 9 cm, height h
h = 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 the length, \( w \) is the width, and \( h \) is the height. Here, \( l = 9 \, \text{cm} \), \( w = 9 \, \text{cm} \), and \( V = 1620 \, \text{cm}^3 \).

Step2: Substitute the known values into the formula

Substitute \( l = 9 \), \( w = 9 \), and \( V = 1620 \) into \( V = l \times w \times h \):
\( 1620 = 9 \times 9 \times h \)
Simplify \( 9 \times 9 = 81 \), so the equation becomes \( 1620 = 81 \times h \).

Step3: Solve for \( h \)

To find \( h \), divide both sides of the equation by 81:
\( h = \frac{1620}{81} \)
Calculate \( \frac{1620}{81} = 20 \).

Answer:

20