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The diameter and the slant height of a cone are both 24 cm. Find the radius of the largest sphere that can be placed inside the...Question
300. The diameter and the slant height of a cone are both 24 cm. Find the radius of the
largest sphere that can be placed inside the cone. (The sphere is therefore tangent to the
base of the cone.) The sphere occupies a certain percentage of the cone’s volume. First
estimate this percentage, then calculate it.
largest sphere that can be placed inside the cone. (The sphere is therefore tangent to the
base of the cone.) The sphere occupies a certain percentage of the cone’s volume. First
estimate this percentage, then calculate it.
Answers
oobleck
To find the radius of the sphere, this article will help.
https://math.stackexchange.com/questions/3079286/sphere-inscribed-in-a-cone
The proportion shown gives the formula
R = radius of cone
h = height of cone
r = radius of sphere
√(R^2+h^2) / R = (h-r)/r
Knowing r, you can easily get the volume.
https://math.stackexchange.com/questions/3079286/sphere-inscribed-in-a-cone
The proportion shown gives the formula
R = radius of cone
h = height of cone
r = radius of sphere
√(R^2+h^2) / R = (h-r)/r
Knowing r, you can easily get the volume.
5.35