Question

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Volume of Pyramids Quick Check
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Question
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

20.80 in.3
20.80 in. cubed

6.93 in.3
6.93 in. cubed

9.01 in.3

Answer 1

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 square base, the base area can be calculated as:

\[
\text{Base Area} = \text{side}^2
\]

Given that the dimensions are 2.75 in. for the length of the base and the height (assuming the height is also given as 2.75 in.), we first calculate the base area:

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

Next, we can substitute this and the height into the volume formula:

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

Calculating this step-by-step:

1. First compute \(7.5625 \times 2.75\):

\[
7.5625 \times 2.75 = 20.803125
\]

2. Now, calculate the volume:

\[
V = \frac{1}{3} \times 20.803125 \approx 6.934375
\]

Rounding to the nearest hundredth:

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

Thus, the correct response is:

**6.93 in.³**