Question

The diameters of two cones are equal. If their slant heights are 7:4, find the ratio of their curved surface area

Answer 1

Solution:-

Since the diameters of two cones are equal, their radius will also be the same.
Let the slant height of the two cones be l₁ and l₂ respectively.

Therefore,
l₁ : l₂ = 7 : 4
The curved surface area of the two cones are 
πrl₁ and πrl₂
So, the ratio of their curved surface area are
πrl₁/πrl₂
π and r are cancelled.
⇒ l₁/l₂ = 7/4
So, the ratio of the curved surface area of two cones is 7 : 4
Answer.

Answer 2

diameter of cones are equal it means radius will also be equal
r1=r2
slant height ratio is given l1/l2=7/4
curved surface area of cone = pi*r*l
r is the radius and l is slant height
ratio of their curved surface area=pi*r1*l1 / pi*r2*l2
                                                     =l1/l2  (since r1=r2)
                                                      =7/4            ANSWER