Question
What is the volume of a square pyramid with a base length of 6 cm and a height of 9 cm? G.11C
Question 1 options:
324 cm³
108 cm³
18 cm³
36 cm³
Answers
Answered by
GPT-4o mini
To find the volume \( V \) of a square pyramid, you can use the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
The base area \( A \) of a square pyramid is calculated as:
\[
A = \text{Base Length}^2
\]
In this case, the base length is 6 cm, so:
\[
A = 6 \, \text{cm} \times 6 \, \text{cm} = 36 \, \text{cm}^2
\]
Now, you can plug the base area and height into the volume formula. The height is given as 9 cm:
\[
V = \frac{1}{3} \times 36 \, \text{cm}^2 \times 9 \, \text{cm}
\]
Calculating that:
\[
V = \frac{1}{3} \times 36 \times 9 = \frac{324}{3} = 108 \, \text{cm}^3
\]
Thus, the volume of the square pyramid is:
\[
\boxed{108 \, \text{cm}^3}
\]
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
The base area \( A \) of a square pyramid is calculated as:
\[
A = \text{Base Length}^2
\]
In this case, the base length is 6 cm, so:
\[
A = 6 \, \text{cm} \times 6 \, \text{cm} = 36 \, \text{cm}^2
\]
Now, you can plug the base area and height into the volume formula. The height is given as 9 cm:
\[
V = \frac{1}{3} \times 36 \, \text{cm}^2 \times 9 \, \text{cm}
\]
Calculating that:
\[
V = \frac{1}{3} \times 36 \times 9 = \frac{324}{3} = 108 \, \text{cm}^3
\]
Thus, the volume of the square pyramid is:
\[
\boxed{108 \, \text{cm}^3}
\]
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