Question

If the radius and slant height of a cone are in the ratio 7 : 13 and its curved surface area is 286 cm², find its radius.

Answer 1

The radius of the cone is equal to 7 cm.

Let the radius of the cone be equal to r and the slant height of the cone be equal to l.

Given that the ratio of the radius of the cone and the slant height is 7/13 , r/l = 7/13

=> l = 13r/7

Curved surface area of the cone = 286 cm²

=> πrl = 286

=> (22/7) × 13r²/7 = 286 [l = 13r/7]

=> r² = 49

=> r = 7cm

The radius of the cone = 7 cm

Answer 2

The radius of a cone (r) = 7 cm

Step-by-step explanation:

Given,

The curved surface area (CSA) of cone = 286 $cm^2$ and

Let the radius of a cone(r) = 7x and

The slant height of a cone(l) = 13x

To find, the radius of a cone (r) = ?

We know that,

The curved surface area (CSA) of right circular cone = $\pi rl$

∴ $\dfrac{22}{7} 7x\times 13x$ = 286

⇒ $22\times x\times 13x$ = 286

⇒ $13x^2$ = $\dfrac{286}{22}$

⇒ $13x^2$ = 13

⇒ $x^2$ = 1

∴ The radius of a cone (r) = 7 × 1 cm = 7 cm

Thus, the radius of a cone (r) is equal to "7 cm".