Problema Solution
1. 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. Ans. 4.63 cm
Answer provided by our tutors
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:
(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
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click here to see the equation solved for R
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R = 4.64 cm
The radius of the cone is 4.64 cm.