Question

A cone has a radius of 24 cm and a volume of 1,920 cm cubed. What is the Volume of a similar cone with a radius of 18 cm?

a) 480 cm cubed
b) 810 cm cubed
c) 1,080 cm cubed
d) 1,440 cm cubed

Answer 1

24 * 3/4 = 18

The radius of smaller cone is 3/4 the radius of original cone, so since these cones are similar, height must also be 3/4 times smaller.

So since radius is squared and we also multiple the height (V = 1/3 π r² h),
the volume of smaller cone would be 3³ / 4³ = 27 / 64 times smaller

So we have 1920 * (27 / 64) = 810.

Final answer: B