Question

The diameters of two cones are equal.If their slant heights are in the ratio 5:4,the ratio of their curved surface areas, is

• A. 4:5
• B. 25:16
• C. 16:25
• D. 5:4

Answer 1

The correct option is D

5:4

$\because$ Diameters of two cones are equal, their radii are also equal.

Let r be their radius of each cone,and ratio in their slant heights = 5:4

Let slant height of first cone ($l_1)$ = 5x

Then height of second cone ($l_2)$ = 4x

Hence, $\frac{Curvedsurfaceareaoffirstcone}{Curvedsurfaceareaofsecondcone}=\frac{\pi r\left(5x\right)}{\pi r\left(4x\right)}=\frac{5x}{4x}=\frac{5}{4}\therefore Ratio=5:4$