Two similar cones have heights of 3 feet and 12 feet. The volume of the small cone is 21 cubic inches. What is the volume of the larger cone?

Question

what is the volume of the larger cone?

Answer 1

The volume of a cone is given by:

V = pi * r^2 * h / 3

Since the cones are similar, r (the radius of the base) will scale with h (the height) so the volume will scale with the third power of h. We can therefore write the volume of the 12 ft cone as:

V(12 ft cone) = V(3 ft cone) * (12/3)^3 = 21 in^3 * 4^3 = 1,344 in^3

Answer 2

So a cone has a right angle measurement in it such that

h1/b1=h2/b2

the volume of a cone is pi*r^2*h/3

from this, you need to find the radius which is base 1

then you put that into h1/b1=h2/b2

and find base 2, which is the radius of the other cone. From there just plug into volume