Question

The radius and slant height of acone are in the ratio of 3:5 it its curved surface area is 2310 cm2. find its radius
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Answer 1

Given

The radius and slant height of acone are in the ratio of 3:5 it its curved surface area is 2310 cm².

We Find

It's Radius

We Know

Curved Surface Area of Cone is :-

$\sf \boxed {\red{ \frac{22}{7} \times Radius \times Lenght }}$

According to the question

Let the radius and height is 3x and 5x,

$\implies \sf { \frac{22}{7} \times Radius \times Lenght = CSA\:of\:Cone}$

$\implies \sf { \frac{22}{7} \times 3x \times 5x = 2310 cm²}$

$\implies\sf { 15x² = \frac{2310 × 7}{22} }$

$\implies\sf { 15x² = \frac{16,170}{22} }$

$\implies\sf { 15x² = \cancel\frac{16,170}{22} }$

$\implies \sf { 15x² = 735 }$

$\implies \sf { x² = \frac{735}{15} }$

$\implies\sf { x² = \cancel\frac{735}{15} }$

$\implies\sf { x² = 49 }$

$\implies \sf { x = \sqrt{49} }$

$\implies \sf {\red{\underline{\underline{ x = 7 }}}}$

So, Value of x is 7 cm

☆ Radius = 3 × 7 = 21 cm

☆ Height = 5 × 7 = 35 cm

Hence, Radius of Given Cone is 21 CM.