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