# Two similar cones have volumes 12picu. units and 96pi cu. units. if the curved surface area of smaller cone is 15pi square units, what is curved surface area of larger one

2
Log in to add a comment

Log in to add a comment

i.e.

v/V =((1/3)π r² h)/((1/3)π R² H)

⇒12π/96π = r²h/R²H = r³/R³ ( as the ratio is same)

⇒r³/R³ =1/8

C.S.A1/C.S.A2 = (πr l)/(πR L)

⇒15π/C.S.A2 = r²/R² (as the ratio is same )

⇒15π/C.S.A2 =1/4

and bigger one be R=96pi cu.

so if rcu./Rcu.= 12pi/96pi=1/8

r/R=12

and rsq./Rsq.=1/4

therefore we can say that in comparison of their ratios with their csa is

15sq./csa2= 1/4

15×4=csa2

60=csa2

hence csa of larger cone is 60pi sq.