Question

PLEASE HELP!

A cone has a radius of 15 cm and a volume of 540cm^3. What is the volume of a similar cone with a radius of 10 cm?

A) 54 cm^3
B) 240cm^3
C) 160cm^3
D) 360cm^3

Answer 1

if the linear ratio of two similar figures is a/b, then the ratio between there volume is (a/b)^3

Answer 2

recall \(\bf \cfrac{side}{side}=\cfrac{side}{side}\qquad \cfrac{side^2}{side^2}=\cfrac{Area}{Area}\qquad \cfrac{side^3}{side^3}=\cfrac{Voume}{Volume}
\\ \quad \\
\cfrac{r_{cone1}^3}{r_{cone2}^3}=\cfrac{Volume_{cone1}}{Volume_{cone2}}\implies \cfrac{15^3}{10^3}=\cfrac{540}{v}\)