Question

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

Answer 1

As the two cones are similar, so the ratio of their dimensions will be same.
i.e.
r/R = h/H =l/L
now, Volume =(1/3)π r² h
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
⇒r/R =1/2
now, curved surface area = πr l
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
∴C.S.A2 =60π square units
Biggest one has the curved surface area = 60π square units 

Answer 2

Let smaller cone radius be r =12pi cu.
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.