Question

 the diameters of two cones are equal.if their slant heights are in the ratio of 5:4,find the ratio of their curved surface area

Answer 1

ratio of slant height

=slant height of big cone / slant height of small cone

= (π * r * √r^2 + 25)/(π * r * √r^2 + 16)

=(r^2 + 25):(r^2 + 16)

Answer 2

Answer:

5:4

Step-by-step explanation:

We are given that the diameters of two cones are equal

Thus the radii of these two cones will be equal

Their slant heights are in the ratio of 5:4

Let the ratio be x

So, slant heights will be 5x and 4 x

Formula of curved surface area of cone = $\pi r l$

where r is the radius

l is  the slant height

So, Curved surface area of cone whose slant height is 5x = $\pi \times r \times 5x$

Curved surface area of cone whose slant height is 4x = $\pi \times r \times 4x$

So, ratio of their curved surface area = $\frac{\pi \times r \times 5x}{\pi \times r \times 4x}$

                                                             = $\frac{5}{4}$  

Hence the ratio of their curved surface area is 5:4