Answer to Question #149991 in Geometry for yui

Question

PROBLEM 2. A block of wood is in the form of a right circular cone. The altitude is 12 cm and the radius of the base is 5 cm. A cylindrical hole of 5 cm is bored completely through the solid, the axis of the hole coinciding with the axis of the cone. Find the amount of wood left after the hole is bored.
FINAL ANSWER: _______________________________________

Answer 1

Radius of cone is 5 cm

Height of cone is 12 cm

Radius of cylinder is 2.5 cm

Let height of cylinder is h cm

 By similarity

(12-h)/12 = 2.5/5

=> 12 - h = 6

=> h = 6

Now volume of cone = $\frac{1}{3}π(5²)(12)= 100π cm³$

Volume of cylinder inside = $π(2.5²)(6)= 37.5π cm³$

So volume of remaining wood

= (100π - 37.5π ) cm³

= 62.5π cm³

= 196.35 cm³