Question

a rectangular pyramid has the dimensions shown in the diagram. the volume of a rectangular pyramid, ( v ), can be found using ( v = \frac{1}{3}lwh ), where ( l ) is the length of the base, ( w ) is the width of the base, and ( h ) is the height of the pyramid.
diagram of a rectangular pyramid with height labeled 8.4 cm, base length 9.6 cm, base width 7.2 cm
what is the approximate volume of the rectangular pyramid?

a. ( 21.5 , \text{cm}^3 )

b. ( 145.1 , \text{cm}^3 )

c. ( 193.5 , \text{cm}^3 )

d. ( 258.0 , \text{cm}^3 )

e. ( 580.6 , \text{cm}^3 )

Explanation:

Step1: Identify the values of l, w, h

From the diagram, \( l = 9.6 \, \text{cm} \), \( w = 7.2 \, \text{cm} \), \( h = 8.4 \, \text{cm} \).

Step2: Substitute into the volume formula

The formula for the volume of a rectangular pyramid is \( V=\frac{1}{3}lwh \). Substitute the values:
\( V=\frac{1}{3}\times9.6\times7.2\times8.4 \)

Step3: Calculate the product

First, calculate \( 9.6\times7.2 = 69.12 \). Then, \( 69.12\times8.4 = 580.608 \). Then, \( \frac{1}{3}\times580.608 = 193.536 \approx 193.5 \, \text{cm}^3 \).

Answer:

C. \( 193.5 \, \text{cm}^3 \)