The height of a cone is 45 cm. It is cut at a height of 15 cm from its base by a plane parallel to its base. If the volume of the smaller cone is 18480 cm3 , then what is the volume (in cm3 ) of the original cone?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 , i.e. 62370
Height of original cone = 45 cm
Height of smaller cone = 30 cm
Let the radius of bigger and smaller cone be R and r respectively
△ABC~△ADF
AB/AD = BC/DE
h/H = r/R
30/45 = r/R
r/R = 2/3
Volume of smaller cone/ Volume of bigger cone = 18480/V
[1/3 πr2h]/[1/3πR2h] = 18480/V
V = 62370 cm3