Question

what is the exact volume of the largest cone that can fit into a cube with edges of 10 inches?

Answer 1

cube volume = L x L x L = L^3
cone volume = pi x r^2 x h/3
in this case: r = L/2 and h = L
cone volume = pi x (L/2)^2 x L/3
cone volume = pi x L^2/4 x L/3
cone volume = pi x L^3/12

so if L = 10
cube volume = L x L x L = L^3
cube volume = 10 x 10 x 10 = 10^3
cube volume = 1000 in^3

so if L = 10
cone volume = pi x r^2 x h/3
cone volume = pi x L^3/12
cone volume = pi x 10^3/12
cone volume = pi x 1000/12
cone volume = 261.8 ...ish in^3

Answer 2

Thanks, man for your help.

Answer 3

no worries dude