J Juice brand wants to create a new bottle for their products. Their marketing department wants to design a pyramid–shaped bottle with a base that is 8 cm by 15 cm, and has an altitude of 22 cm. How much juice will this new bottle hold?(1 point)

Responses

15 cm3
15 cm cubed

2,640 cm3
2,640 cm cubed

880 cm3
880 cm cubed

7,920 cm3

1 answer

To find the volume of a pyramid-shaped bottle, we can use the formula for the volume of a pyramid:

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

First, we need to calculate the base area of the pyramid. The base is a rectangle with dimensions 8 cm and 15 cm.

\[ \text{Base Area} = \text{length} \times \text{width} = 8 , \text{cm} \times 15 , \text{cm} = 120 , \text{cm}^2 \]

Next, we'll use the height (altitude) of the pyramid, which is given as 22 cm.

Now, substituting the base area and the height into the volume formula:

\[ V = \frac{1}{3} \times 120 , \text{cm}^2 \times 22 , \text{cm} \]

Calculating the volume:

\[ V = \frac{1}{3} \times 120 \times 22 = \frac{1}{3} \times 2640 = 880 , \text{cm}^3 \]

Therefore, the volume of the pyramid-shaped bottle will hold:

\[ \boxed{880 , \text{cm}^3} \]