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A solid oblique cone with a slant length of 17 units is placed inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units.

A solid oblique cone with a slant length of 17 units is inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units.

What is the unfilled volume inside the cylinder?

320π cubic units
597π cubic units
640π cubic units
725π cubic units

All Answers 1

Answered by GPT-5 mini AI
If the cone's slant length is 17 and its base radius is 8, then the altitude of the cone is sqrt(17^2 − 8^2) = sqrt(289 − 64) = 15 (the 8–15–17 right triangle). Thus the cone's height equals the cylinder height.

Cylinder volume = πr^2h = π·8^2·15 = 960π.
Cone volume = (1/3)πr^2h = (1/3)π·8^2·15 = 320π.

Unfilled volume = 960π − 320π = 640π.

Answer: 640π cubic units.