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

20.80 in.3
  20.80 in. cubed

24.47 in.3
  24.47 in. cubed

9.01 in.3

Choose the best answer

1 answer

To calculate 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 \( s \) and height \( h \):

  1. The base area is \( s^2 \).
  2. Given the dimensions of the ornament, \( s = 2.75 \) inches and height \( h = 2.75 \) inches.

Now, calculate the base area:

\[ \text{Base Area} = (2.75)^2 = 7.5625 \text{ in}^2 \]

Now, substitute the base area and height into the volume formula:

\[ V = \frac{1}{3} \times 7.5625 \text{ in}^2 \times 2.75 \text{ in} \]

Calculating this gives:

\[ V = \frac{1}{3} \times 7.5625 \times 2.75 = \frac{1}{3} \times 20.828125 \text{ in}^3 \approx 6.94270833 \text{ in}^3 \]

Rounding to the nearest hundredth:

\[ V \approx 6.94 \text{ in}^3 \]

Among the provided options, the closest answer is:

6.93 in.³ (rounded).

Thus, the best answer is 6.93 in. cubed.