Question
Arturo sketches this square-based pyramid. Each edge of the base measures 8 centimeters, as shown in the image. As well as a height of 10 cm. What is the volume of Arturo’s pyramid, rounded to the nearest whole cubic centimeter?
(1 point)
Responses
213
213
27
27
640
640
214
(1 point)
Responses
213
213
27
27
640
640
214
Answers
GPT-4o mini
To find the volume of a square-based pyramid, you can use the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
1. First, calculate the area of the base. Since the base is a square with each side measuring 8 cm:
\[
\text{Base Area} = \text{side length} \times \text{side length} = 8 \, \text{cm} \times 8 \, \text{cm} = 64 \, \text{cm}^2
\]
2. Next, use the height of the pyramid, which is given as 10 cm.
3. Plug the base area and height into the volume formula:
\[
V = \frac{1}{3} \times 64 \, \text{cm}^2 \times 10 \, \text{cm}
\]
4. Calculate the volume:
\[
V = \frac{1}{3} \times 640 \, \text{cm}^3 = \frac{640}{3} \, \text{cm}^3 \approx 213.33 \, \text{cm}^3
\]
5. Rounded to the nearest whole cubic centimeter, the volume is:
\[
V \approx 213 \, \text{cm}^3
\]
So the answer is **213**.
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
1. First, calculate the area of the base. Since the base is a square with each side measuring 8 cm:
\[
\text{Base Area} = \text{side length} \times \text{side length} = 8 \, \text{cm} \times 8 \, \text{cm} = 64 \, \text{cm}^2
\]
2. Next, use the height of the pyramid, which is given as 10 cm.
3. Plug the base area and height into the volume formula:
\[
V = \frac{1}{3} \times 64 \, \text{cm}^2 \times 10 \, \text{cm}
\]
4. Calculate the volume:
\[
V = \frac{1}{3} \times 640 \, \text{cm}^3 = \frac{640}{3} \, \text{cm}^3 \approx 213.33 \, \text{cm}^3
\]
5. Rounded to the nearest whole cubic centimeter, the volume is:
\[
V \approx 213 \, \text{cm}^3
\]
So the answer is **213**.