Question

The diameters of two cones are equal and their slant heights are in the ratio 5 : 4. If the curved surface area of the smaller cone is 200 cm², then the curved surface area of the bigger cone is _________.

Answer 1

Let l₁ be the slant height of first cone and l₂ be the slant height of the second cone.

Given: l₁ : l₂ = 5 : 4

∴ l₁ = 5x and l₂ = 4x, where x is constant

It is given that the diameters of the two cones are equal. Therefore, the radii of the two cones are equal.

Let the radius of each cone be r cm.

Since the radii of two cones are equal, so the cone with bigger slant height would be bigger than the other.

Now,

Curved surface area of the bigger cone = $\mathrm{\pi }$rl₁

Curved surface area of the smaller cone = $\mathrm{\pi }$rl₂

$\therefore \frac{\mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{bigger}\mathrm{cone}}{\mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{smaller}\mathrm{cone}}=\frac{\mathrm{\pi }r{l}_1}{\mathrm{\pi }r{l}_2}$

$\Rightarrow \frac{\mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{bigger}\mathrm{cone}}{200{\mathrm{cm}}^2}=\frac{l_1}{l_2}=\frac{5x}{4x}$

⇒ Curved surface area of the bigger cone = $\frac{5}{4}\times 200{\mathrm{cm}}^2$ = 250 cm²

Thus, the curved surface area of the bigger cone is 250 cm².

The diameters of two cones are equal and their slant heights are in the ratio 5 : 4. If the curved surface area of the smaller cone is 200 cm², then the curved surface area of the bigger cone is ____250 cm²____.