Question

The ratio of slant height and radius of a cone 7 ratio 4 if its curved surface area is 792 cm square then find its radius.

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\small{\underline{\red{\rm{let:}}}}$

• $\rm{The\: ratio\:of\: slant\: height\:and\: radius\:be\:x}$

$\small{\underline{\red{\rm{Given:}}}}$

• $\rm{C.S.A\:of\:cone=792\:cm^2}$
• $\rm{The\: slant\: height=7x}$
• $\rm{The\: radius\:of\:cone=4x}$

$\small{\underline{\red{\rm{To\: Find:}}}}$

• $\rm{The\: radius\:of\:cone}$

$\small{\underline{\red{\rm{As\:per\:the\: above\: information:}}}}$

$\rm\red{\implies C.S.A=\pi\:r\:l}$

$\rm{\implies \dfrac{22}{7}*4x*7x=792}$

$\rm{\implies 22*4x*x=792}$

$\rm{\implies \cancel{88}x^2=\cancel{792}}$

$\rm{\implies x^2=9}$

$\rm{\implies x=\sqrt{9}}$

$\rm{\implies x=-3\:or\:+3}$

• Negative value can't be kept so we have to take x=+3

Hence,

$\rm\purple{The\: slant\: height=7x=7*3=21\:cm}$

$\rm\green{The\: radius\:of\:cone=4x=4*3=12\:cm}$

Answer 2

Answer:-

Given:

Slant height : Radius = 7 : 4

→ l : r = 7 : 4

CSA of the Cone = 792 cm²

Let Slant height and radius be 7x and 4x.

We know that,

CSA of cone = πrl

→ 22/7 * (4x) * (7x) = 792

→ 88x² = 792

→ x² = 792/88

→ x² = 9

→ x = ± 3

→ 4x = 4(3) or 4(- 3)

→ 12 or - 12

Radius of a Cone cannot be negative, So positive value is taken i.e., 12 cm.

Hence, the radius of the Cone is 12 cm.