Help w/ Another Pythagorean Theorem Question?

Please do #3 and show your work
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1 Answer
P dilip_k
Mar 4, 2018

Maximum radius of the ball =#sqrt10# cm

Explanation:

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The situation as described in the problem No.-3 is represented in above figure. Here three identical spheres each of maximum radius #r# cm fit entirely in the cylindrical can in which the length of the longest nail that can be just placed is 20 cm.

It is obvious from figure that the radius of the cylindrical can must be #r# cm and its height #h=6r#cm.

Applying Pythagorean theorem we can write

#(6r)^2+(2r)^2=20^2#

#=>40r^2=400#

#=>r=sqrt10# cm

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