perplexus.info :: Shapes : Hypotenuse from Cone

Hypotenuse from Cone (Posted on 2016-01-22)

PQR is a right angled triangle, where PR is the hypotenuse.
When this triangle is rotated about PQ, the volume of the cone produced is 800 cubic inches.
When the triangle is rotated about QR, the volume of the cone produced is 1920 cubic inches.

Determine (in inches) the hypotenuse of the triangle.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

same solution numerically

Comment 2 of 2 |

Call side QR, p; and side QP, r.

r*pi*p^2 / 3 = 800

p*pi*r^2 / 3 = 1920

dividing the second equation by the first gives:

r/p = 1920/800 = 12/5

substituting into the first from r = 12*p/5:

12*pi*p^3/15 = 800

p = cuberoot(1000/pi) = 10/cuberoot(pi)

r = 120/(5*cuberoot(pi)) = 24/cuberoot(pi)

hypotenuse = sqrt(100/pi^(2/3) + 576/pi^(2/3)) ~= 17.7523856446377

Posted by Charlie on 2016-01-22 10:42:20

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