Question
A contractor is building one-bedroom cabin homes. There are two designs. One design has a rectangular pyramid shape where the entire inside is living space. The other is a rectangular shape with a roof, with the roof portion not being used for living space. Each cabin has congruent base areas and inside height. If the cabins both have a base area of 144 ft.2
144
ft
.
2
, and height of 9 ft., what is the volume of the pyramid-shaped cabin?(1 point)
Responses
48 ft.3
48
ft
.
3
48 ft . cubed
432 ft.3
432
ft
.
3
432 ft. cubed
1,296 ft.3
1
,
296
ft
.
3
1,296 ft. cubed
16 ft.3
144
ft
.
2
, and height of 9 ft., what is the volume of the pyramid-shaped cabin?(1 point)
Responses
48 ft.3
48
ft
.
3
48 ft . cubed
432 ft.3
432
ft
.
3
432 ft. cubed
1,296 ft.3
1
,
296
ft
.
3
1,296 ft. cubed
16 ft.3
Answers
GPT-4o mini
To calculate the volume of the pyramid-shaped cabin, we can use the formula for the volume \( V \) of a pyramid:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that the base area is \( 144 \, \text{ft}^2 \) and the height is \( 9 \, \text{ft} \), we can substitute these values into the formula:
\[
V = \frac{1}{3} \times 144 \, \text{ft}^2 \times 9 \, \text{ft}
\]
Calculating the volume:
\[
V = \frac{1}{3} \times 144 \times 9
\]
\[
V = \frac{1}{3} \times 1296
\]
\[
V = 432 \, \text{ft}^3
\]
Thus, the volume of the pyramid-shaped cabin is \( \boxed{432 \, \text{ft}^3} \).
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that the base area is \( 144 \, \text{ft}^2 \) and the height is \( 9 \, \text{ft} \), we can substitute these values into the formula:
\[
V = \frac{1}{3} \times 144 \, \text{ft}^2 \times 9 \, \text{ft}
\]
Calculating the volume:
\[
V = \frac{1}{3} \times 144 \times 9
\]
\[
V = \frac{1}{3} \times 1296
\]
\[
V = 432 \, \text{ft}^3
\]
Thus, the volume of the pyramid-shaped cabin is \( \boxed{432 \, \text{ft}^3} \).