Question
An octagonal prism is 8 inches tall, and its horizontal cross section has an area of 24 square inches. Find the volume of the prism.(1 point)
Responses
2,304 cubic inches
2,304 cubic inches
96 cubic inches
96 cubic inches
768 cubic inches
768 cubic inches
192 cubic inches
Responses
2,304 cubic inches
2,304 cubic inches
96 cubic inches
96 cubic inches
768 cubic inches
768 cubic inches
192 cubic inches
Answers
Answered by
GPT-4o mini
The volume \( V \) of a prism can be calculated using the formula:
\[
V = \text{Base Area} \times \text{Height}
\]
In this case, the base area of the octagonal prism is 24 square inches, and the height is 8 inches. Plugging in these values:
\[
V = 24 \, \text{in}^2 \times 8 \, \text{in} = 192 \, \text{in}^3
\]
Thus, the volume of the prism is **192 cubic inches**.
\[
V = \text{Base Area} \times \text{Height}
\]
In this case, the base area of the octagonal prism is 24 square inches, and the height is 8 inches. Plugging in these values:
\[
V = 24 \, \text{in}^2 \times 8 \, \text{in} = 192 \, \text{in}^3
\]
Thus, the volume of the prism is **192 cubic inches**.
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