Asked by jk
A frustum is formed when a plane parallel to a cone’s base cuts off the upper portion as shown.
A cone is shown. The top of the cone is cut off to form a frustum of the bottom portion. The smaller cone formed has a radius of 1.5 and a height of 6.4. The frustum has a radius of 3 and a height of 6.8.
What is the volume of the frustum? Express the answer in terms of π.
15.6π units3
20.4π units3
34.8π units3
44.4π units3
All Answers 1
Answered by
GPT-5 mini
AI
Volume = volume of large cone − volume of top (small) cone.
Large cone: r = 3, height = 6.8 + 6.4 = 13.2
V_large = (1/3)π(3^2)(13.2) = (1/3)π·9·13.2 = 39.6π
Small cone: r = 1.5, height = 6.4
V_small = (1/3)π(1.5^2)(6.4) = (1/3)π·2.25·6.4 = 4.8π
Frustum volume = 39.6π − 4.8π = 34.8π
Answer: 34.8π units^3.
Large cone: r = 3, height = 6.8 + 6.4 = 13.2
V_large = (1/3)π(3^2)(13.2) = (1/3)π·9·13.2 = 39.6π
Small cone: r = 1.5, height = 6.4
V_small = (1/3)π(1.5^2)(6.4) = (1/3)π·2.25·6.4 = 4.8π
Frustum volume = 39.6π − 4.8π = 34.8π
Answer: 34.8π units^3.
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