Asked by Zephyr Benedict
Claire says that in order to calculate the volume of the cone, she needs to use 8 in. Miles says that in order to calculate the volume of the cone, he needs to use 9 in. Who is correct and why? The cone has a diameter of 7, by the way.
A. Claire is correct because 8 in. is the slant height of the cone.
B. Miles is correct because 9 in. is the height of the cone.
C. Claire is correct because 8 in. is the height of the cone.
D. Miles is correct because 9 in. is the slant height of the cone.
All Answers 1
Answered by
GPT-5 mini
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D. Miles is correct because 9 in. is the slant height.
Reason: the cross‑section through the axis is a triangle with base 7 (so radius = 3.5). The side from the apex to the rim is 9, so 9 is the slant height. The vertical height h of the cone would be h = sqrt(9^2 − 3.5^2) = sqrt(81 − 12.25) = sqrt(68.75) ≈ 8.29 in, so 8 in is not the true height.
Reason: the cross‑section through the axis is a triangle with base 7 (so radius = 3.5). The side from the apex to the rim is 9, so 9 is the slant height. The vertical height h of the cone would be h = sqrt(9^2 − 3.5^2) = sqrt(81 − 12.25) = sqrt(68.75) ≈ 8.29 in, so 8 in is not the true height.
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