Question

The radius and slant height of
Alar cone are in the ratio 7:13and it's curved
surface area is 286cm. Find its radius


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Answer 1

Answer- The above question is from the chapter 'Surface Areas and Volumes'.

For a cone,

Let radius (r) be 7x and slant height (l) be 13x.

Curved surface area (CSA)= 286 cm²

We know that curves surface area of a cone is πrl .

πrl = 286 cm²

22/7 × 7x × 13x= 286

22× 13 x²= 286

x²= 286 ÷ 286

x²= 1

x= ±√1

x= ±1 cm

x= 1 cm (Rejected -1 cm ∵ x can't be negative.)

Slant height (l)= 13x= 13 cm

∴Radius= 7x= 7 cm

Answer 2

$\huge\mathfrak\green{Heyaa!!}$

$\huge\mathfrak\red{Answer:-}$

We have been given that the ratio of radius and slant height of Alar cone is in the ratio of 7: 13

Let us assume that the radius of cone be 7a and height be 13a.

Then the curved surface area=

$\pi \times rl = \pi(</em><em>7a</em><em>) \times (</em><em>13a</em><em>)$

$= 91ra ^{2} = 286$

$or \: a ^{2} = 286 \div 91 \times 7 \div 22 = 1$

$</em><em>a</em><em> = 1$

$= > radius \: of \: cone = 7cm$