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MATH / A sphere is inscribed in a cone with height 4 and base radius 3. What is the…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A sphere is inscribed in a cone with height 4 and base radius 3.  What is the ratio of the volume of the sphere to the volume of the cone?

[asy]
fill(circle((1.5,0),1.5),gray(.7));
draw((0,3)--(4,0)--(0,-3));
draw(circle((1.5,0),1.5));
draw((0,0)..(1.5,-.3)..(3,0));
draw((0,0)..(1.5,.3)..(3,0),dashed);
draw(xscale(.15)*circle((0,0),3));
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
5aece9a5-825e-5e0f-9141-de2e1a891c88
task_key
geometry--test--5aece9a5-825e-5e0f-9141-de2e1a891c88
task_revision_id
1
config / split
geometry / test

Official source

initial import