Question

A cone 12cm high is cut 8cm from the vertex to form a frustum with a volume of 190cu.cm. Find the radius of the cone.

Answer 1

h = 12 - 8

h = 4 cm

V = 190 cm^3

R = the radius of the cone

r = the radius of the piece that is cut off

R : r = 12 : 8

12r = 8R

r = (8/12)R

r = (2/3)R

Plug into the volume formula:
Now the volume of the frustum cone

=(π/3)h(R^2+r^2+R^r)

(pi/3)*4(R^2 + (4/9)R^2 + (2/3)R^2) = 190

(R^2)*pi*(4/3)(1 + 4/9 + 2/3) = 190

pi = 3.14

(R^2)*3.14*(4/3)(1 + 4/9 + 2/3) = 190

4.19×19/9R^2 =190

R^2=(190×9)/(19×4.19)=1710/79.61
=21.48
=>R = 4.64 cm

The radius of the cone is 4.64 cm.