Question

The radius and the slant height of a cone are in the ratio of 4 : 7. If its curved area is 792 cm2 , then its radius will be - (1) 9 cm (2) 6 cm (3) 12 cm (4) 15 cm

Answer 1

The answer is given below :

The ratio of the radius and slant height of the cone = 4 : 7

Let, the common multiple = x.

Then, radius is = 4x cm
and slant height = 7x cm

Given that,

curved area = 792 cm²

=> π × radius × slant height = 792

=> π × 4x × 7x = 792

=> 28πx² = 792

=> x² = 9

=> x = 3, where we take the positive value only.

So, the radius of the base of the cone = 12 cm.

Thank you for your question.

Answer 2

Hiii!!!

Here's ur answer...

ATQ,

The radius and length (slant height) of the cone are in ratio 4 : 7

Let the radius be 4x and length be 7x.

CSA (curved surface area) of the cone = 792cm²

Therefore πrl = 792cm²

==> 22/7 × 4x × 7x = 792cm²

==> 28x² = 792/1 × 7/22

==> 28x² = 36 × 7

==> 28x² = 252

==> x² = 252/28

==> x² = 9

==> x = √9

==> x = 3cm

Therefore, radius of the cone = 4x

= 4 × 3

= 12cm

And length (slant height) of the cone is = 7x

= 7 × 3

= 21cm

Verification :-

CSA of the cone = πrl

= 22/7 × 12 × 21

= 22 × 12 × 3

= 792cm²

Hence verified

Final answer :-

Option (3) 12cm is correct answer...

Hope this helps..!!