A holiday ornament in the shape of a square pyramid has the following dimensions: 2.75 x 2.75 x 2.75 in. What is the approximate volume of the ornament? Round your answer to the nearest hundredth.(1 point)

Responses

6.93 in.3
6.93 in. cubed

24.47 in.3
24.47 in. cubed

20.80 in.3
20.80 in. cubed

9.01 in.3

1 answer

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

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

In this case, the base of the pyramid is a square with dimensions \(2.75 , \text{in} \times 2.75 , \text{in}\).

  1. First, calculate the area of the base: \[ \text{Base Area} = \text{side}^2 = (2.75 , \text{in})^2 = 7.5625 , \text{in}^2 \]

  2. Now, use the height, which is also \(2.75 , \text{in}\): \[ \text{Height} = 2.75 , \text{in} \]

  3. Substitute the values into the volume formula: \[ \text{Volume} = \frac{1}{3} \times 7.5625 , \text{in}^2 \times 2.75 , \text{in} \]

  4. Calculate the volume: \[ \text{Volume} = \frac{1}{3} \times 7.5625 \times 2.75 = \frac{1}{3} \times 20.80 = 6.9333 , \text{in}^3 \]

  5. Finally, rounding to the nearest hundredth: \[ \text{Volume} \approx 6.93 , \text{in}^3 \]

Thus, the approximate volume of the ornament is 6.93 in.³.