Find the volume of a pyramid that has a rectangular base that measures 12 ft. in length and 16 ft. in width and has a height of 24 ft.(1 point)

Question

Responses

4,608 ft.3
4,608 ft. cubed

2,304 ft.3
2,304 ft. cubed

1,536 ft.3
1,536 ft. cubed

1,536 ft.

Answer 1

The volume \( V \) of a pyramid can be calculated using the formula:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

1. First, calculate the area of the rectangular base:

   • Length = 12 ft
   • Width = 16 ft

   \[ \text{Base Area} = \text{Length} \times \text{Width} = 12 , \text{ft} \times 16 , \text{ft} = 192 , \text{ft}^2 \]

2. Next, use the height of the pyramid:

   • Height = 24 ft

3. Now substitute these values into the volume formula:

   \[ V = \frac{1}{3} \times 192 , \text{ft}^2 \times 24 , \text{ft} \]

   \[ V = \frac{1}{3} \times 4608 , \text{ft}^3 = 1536 , \text{ft}^3 \]

Thus, the volume of the pyramid is \( \boxed{1536 , \text{ft}^3} \).