Question

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)
880 cm3 880 cm3
2, 640 cm
3 2, 640 cm3
7, 920 cm3 7, 920 cm3
15 cm3

Answer 1

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

\[
V = \frac{1}{3} \times B \times h
\]

where:
- \( V \) is the volume,
- \( B \) is the area of the base,
- \( h \) is the height (or altitude).

First, we'll calculate the area of the base. The base is a rectangle with a length of 15 cm and a width of 8 cm:

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

Now we can substitute the values into the volume formula. The height of the pyramid is given as 22 cm.

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

Calculating this step-by-step:

1. Calculate \( \frac{1}{3} \times 120 \):
\[
\frac{120}{3} = 40
\]

2. Now multiply by the height \( 22 \):
\[
V = 40 \, \text{cm}^2 \times 22 \, \text{cm} = 880 \, \text{cm}^3
\]

Therefore, the new bottle will hold **880 cm³** of juice.