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प्रश्न
The ratio of the radii of two right circular cones of the same height is 1 : 3. Find the ratio of their curved surface area when the height cone is 3 times the radius of the smaller cone.
उत्तर
Let the radius of the first cone be ‘x’ and the Height of the cone be 3x
l = `sqrt("h"^2 + "r"^2)`
= `sqrt((3x)^2 + x^2)`
= `sqrt(10x^2)`
C.S.A. of the first cone = πrl sq.units
= `pi xx x sqrt(10x^2)`
= `pi x^2 sqrt(10)`
The radius and the height of the second cone is 3x ...(Given)
l = `sqrt((3x)^2 + (3x)^2)`
= `sqrt(9x^2 + 9x^2)`
= `sqrt(18x^2)`
C.S.A of the second one
= `pi xx 3x xx sqrt(18x^2)`
= `pi xx 3x^2 xx sqrt(9 xx 2)`
= `pi 9x^2 sqrt(2)`
Ratio of the curves surface area
= `pix^2 sqrt(10) : 9 pi x^2 sqrt(2)`
= `sqrt(10) : 9sqrt(2)`
= `sqrt(2) xx sqrt(5) : 9sqrt(2)`
= `sqrt(5) : 9`
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