Two cones are similar. The volume of the larger cone is 27 cm³ and the volume of the smaller cone is 8 cm³. The height of the smaller cone is 2 cm.

What is the height of the larger cone?

Question

Two cones are similar. The volume of the larger cone is 27 cm³ and the volume of the smaller cone is 8 cm³. The height of the smaller cone is 2 cm.

What is the height of the larger cone?

Hanna · Answer

Volume of cone, V = (1/3)πr^2h

let H, h and R and r are height and radius of larger and smaller cones respectively

(1/3)πR^2 H /(1/3)πr^2 h = (27/8)

=> R^2 H / r^2 h = (27/8)
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eqn(1)

since cones are similar

R/r = H/h ==> R^2 /r^2 = H^2 /h^2

substitute in eqn (1)

H^3 /h^3 = (27/8)

H/h = 3/2

since h = 2 cm

H/2 = 3/2

=> H = 3 cm

Hope that helps. :)