Question

Cone A has a radíus 12 inches and Cone B has a

radius of 30 inches. If the cones are similar and
the volume of Cone A is 48 ft², find the volume b of Cone b

Answer 1

Check the picture below.

`\cfrac{\stackrel{A~radius}{(12)^3}}{\underset{B~radius}{(30)^3}}~~ = ~~\cfrac{\stackrel{A~volume}{48}}{\underset{B~volume}{V}}\implies \cfrac{1728}{27000}~~ = ~~\cfrac{48}{V}\implies \cfrac{8}{125}~~ = ~~\cfrac{48}{V} \\\\\\ 8V=(48)(125)\implies V=\cfrac{(48)(25)}{8} \\\\\\ V=\cfrac{48}{8}25\implies V=6(25)\implies V=150`