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 24.47 in.3 24.47 in. cubed 6.93 in.3 6.93 in. cubed 20.80 in.3 20.80 in. cubed 9.01 in.3

1 answer

To find the volume of a square pyramid, we 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 \( h \):

  • Base Area \( = s^2 \)
  • Height \( h = 2.75 \) in.

Given that the base is a square with side length of \( s = 2.75 \) in., we calculate the base area:

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

Now we can substitute the values into the volume formula:

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

Now perform the multiplication:

\[ V = \frac{1}{3} \times 20.816875 , \text{in}^3 \]

Calculating the final volume:

\[ V = \frac{20.816875}{3} \approx 6.93895833 , \text{in}^3 \]

Rounding this to the nearest hundredth gives:

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

Thus, among the choices given, the approximate volume of the ornament is:

6.93 in.³