Question

Two cones have the same diameters of the base. The ratio of their slant heights is $5:4.$ If the lateral surface area of the smaller cone is $400{cm}^2$. find the lateral surface area of the larger cone.

Answer 1

Given,
Two cones have the same base diameters. So their radii will also be equal.
Let $r_1=r_2=r$
Let the slant heights $S$ be $l_1$ and $l_1$ then according to the question. $\frac{l_1}{l_2}=\frac{5}{4}$
And lateral surface area of smaller cone $\left(\pi r{l}_2\right)=400{cm}^2$
$=\frac{\text{lateral surfarce area of larger cone}}{\text{lateral surface area of smaller cone}}$
lateral surface area of larger cone $=\frac{l_1}{l_2}\times 400$
$=\frac{4}{5}\times 100=500{cm}^2$