The volume \( V \) of a pyramid is calculated using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
The volume \( V \) of a rectangular prism is calculated using the formula:
\[ V = \text{Base Area} \times \text{Height} \]
Step 1: Calculate the Base Area
For both the pyramid and prism, the base is a rectangle with dimensions 4 inches and 5 inches. Thus, the base area \( A \) is:
\[ A = \text{Length} \times \text{Width} = 4 , \text{in} \times 5 , \text{in} = 20 , \text{in}^2 \]
Step 2: Calculate the Height of the Pyramid
We know the volume of the pyramid is given as 40 in³. Using the volume formula for the pyramid:
\[ 40 = \frac{1}{3} \times 20 \times h \]
To find the height \( h \), we can rearrange the equation:
\[ 40 = \frac{20h}{3} \]
Multiplying both sides by 3:
\[ 120 = 20h \]
Now, divide both sides by 20:
\[ h = \frac{120}{20} = 6 , \text{in} \]
Step 3: Calculate the Height of the Prism
We know the volume of the prism is given as 120 in³. Using the volume formula for the prism:
\[ 120 = 20 \times H \]
To find the height \( H \), we rearrange the equation:
\[ H = \frac{120}{20} = 6 , \text{in} \]
Summary
The height of both the rectangular pyramid and the rectangular prism is:
\[ \text{Height} = 6 , \text{in} \]