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.
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 20160122 10:42:20 