A goofy ahh 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

6.93 in.3
6.93 in. cubed

24.47 in.3

1 answer

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

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

In this case, the base area of the pyramid is a square with side length of 2.75 inches. Thus, the area of the base is:

\[ \text{Base Area} = \text{side}^2 = 2.75 \times 2.75 = 7.5625 , \text{in}^2 \]

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

Now, plug these values into the volume formula:

\[ V = \frac{1}{3} \times 7.5625 \times 2.75 \]

Calculating this step-by-step:

  1. Multiply the base area by the height: \[ 7.5625 \times 2.75 \approx 20.80 \]

  2. Now divide by 3 to get the volume: \[ V = \frac{20.80}{3} \approx 6.9333 \]

Rounding to the nearest hundredth gives:

\[ V \approx 6.93 , \text{in}^3 \]

Thus, the answer is:

6.93 in.³