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

9.01 in.3
9.01 in. cubed

20.80 in.3
20.80 in. cubed

6.93 in.3

1 answer

The volume \( V \) of a square pyramid can be calculated using the formula:

\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \]

For a square pyramid, the base area is given by the square of the length of one side of the base. In this case, since the base is a square with dimensions 2.75 in by 2.75 in, we can calculate the base area as follows:

\[ \text{base area} = \text{side}^2 = (2.75 \text{ in})^2 = 7.5625 \text{ in}^2 \]

The height of the pyramid is also given as 2.75 in.

Now substituting these values into the volume formula:

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

Calculating the volume:

\[ V = \frac{1}{3} \times 7.5625 \times 2.75 \] \[ = \frac{1}{3} \times 20.80 \] \[ = 6.9333\ldots \text{ in}^3 \]

Rounded to the nearest hundredth, the volume of the ornament is approximately:

\[ \boxed{6.93} \text{ in}^3 \]