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

20.80 in.3
20.80 in. cubed

9.01 in.3
9.01 in. cubed

24.47 in.3
24.47 in. cubed

6.93 in.3
6.93 in. cubed

1 answer

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

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

For a square pyramid with a base side length of \( s \) and a height \( h \):

  1. Calculate the base area (which is a square): \[ \text{Base Area} = s^2 \] Since the dimensions given are 2.75 inches, we have: \[ \text{Base Area} = (2.75)^2 = 7.5625 , \text{in}^2 \]

  2. The height of the pyramid is also 2.75 inches.

  3. Now, plug these values into the volume formula: \[ V = \frac{1}{3} \times 7.5625 \times 2.75 \]

Calculating this:

First, multiply the base area by the height: \[ 7.5625 \times 2.75 = 20.80 , \text{in}^3 \]

Now, divide by 3 to get the volume: \[ V = \frac{20.80}{3} \approx 6.9333 , \text{in}^3 \]

Rounding to the nearest hundredth, the volume is: \[ \approx 6.93 , \text{in}^3 \]

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