Question

the csa of a right circular cone is twice that of another right circular cone. if the slant height of the second cone is twice that of the first cone;find the ratio of the radius of first cone to that of second cone.

Answer 1

We know that curved surface area of the cone = πrl.

Let the radii be r₁ and r₂.

(i)

Given that one right circular cone is twice that of another circular cone.

⇒ (πr₁l₁)/(πr₂l₂) = 2/1

(ii)

Given that slant height of the second cone is twice that of first cone.

⇒ (πr₁l₁)/(πr₂(2l₁)) = 2/1

⇒ (r₁)/(2r₂) = 2/1

⇒ r₁ = 4r₂

⇒ (r₁)/(r₂) = 4/1

Therefore, the ratio is  4 : 1.

Hope it helps!

Answer 2

let r1 , r2 be the radii and l1 , l2 be the slant heights of two right circular cone .

since,we know CSA of cone = πrl

let ,CSA of first right circular cone

= πr1l1

CSA of second right circular cone

= πr2l2

CSA of first cone = 2× CSA of second cone

πr1l1 = 2 × πr2l2

πr1l1 = 2πr2l2

slant height of second right circular cone

l2 = 2 × slant height of first cone

l2 = 2× l1 = 2l1

πr1l1 = 2πr2 (2l1 )

r1l1 = 4r2l1

r1 = 4r2 => r1 / r2 = 4 / 1

r1 : r2 = 4 : 1

Answer:
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ratio of their radii = 4 : 1
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