Volume of Pyramids Quick Check

Question

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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)
Responses

15 cm3
15 cm cubed

7,920 cm3
7,920 cm cubed

880 cm3
880 cm cubed

2,640 cm3

Answer 1

To find the volume of a pyramid, you can use the formula:

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

1. Calculate the base area of the pyramid:

   • The base is a rectangle with dimensions \(8 , \text{cm}\) and \(15 , \text{cm}\).
   • Base Area = \(8 \times 15 = 120 , \text{cm}^2\)

2. The height (altitude) of the pyramid is \(22 , \text{cm}\).

3. Now, plug these values into the volume formula: \[ \text{Volume} = \frac{1}{3} \times 120 , \text{cm}^2 \times 22 , \text{cm} = \frac{1}{3} \times 2640 , \text{cm}^3 \] \[ \text{Volume} = 880 , \text{cm}^3 \]

Thus, the new bottle will hold 880 cm³ of juice.