The ratio between the curved surface area and the total surface area of a right circular cone is 1:2 . Find the ratio between the height and radius

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Solution

given, csa : tsa of cone = 1:2
πrl / πr(r+l) = 1/2
l/(r+l) = 1/2
by cross multiplication, we get
2l= r+l
2l-l = r
therefore l=r
by calculating, we get height is equal to radius. then ratio of their slant height and radius is
Slant height of cone : radius of cone = 1:1
Hope it helps

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The ratio between the curved surface area and the total surface area of a right circular cone is 1:2 . Find the ratio between the height and radius

given, csa : tsa of cone = 1:2 πrl / πr(r+l) = 1/2 l/(r+l) = 1/2 by cross multiplication, we get 2l= r+l 2l-l = r therefore l=r by calculating, we get height is equal to radius. then ratio of their slant height and radius is Slant height of cone : radius of cone = 1:1 Hope it helps

given, csa : tsa of cone = 1:2
πrl / πr(r+l) = 1/2
l/(r+l) = 1/2
by cross multiplication, we get
2l= r+l
2l-l = r
therefore l=r
by calculating, we get height is equal to radius. then ratio of their slant height and radius is
Slant height of cone : radius of cone = 1:1
Hope it helps