A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.
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Answer:
The Ratio of the surface area of Cylinder and cone is 17 : 9
Step-by-step explanation:
Given :
Base of a right circular Cone & right circular Cylinder are equal then their Radius are also equal.
Radius(r) of the base and height (h) of the Cone & Cylinder are same .
Ratio of radius of the base and height are 5 : 12 i.e r = 5x & h = 12x
Slant height of a cone, l = √r² + h²
l = √(5x)² + (12x)²
l = √25x² + 144x²
l = √169x²
l = 13x
Surface area of Cylinder (S1) / Surface area of cone (S2) = 2πr(h + r) /πr(l + r)
S1/S2 = 2πr(h + r) /πr(l + r)
S1/S2 = 2(h + r) /(l + r)
S1/S2 = 2(12x + 5x) / (13x + 5x)
S1/S2 = 2(17x) /18x
S1/S2 = 17x/9x
S1/S2 = 17/9
S1 : S2 = 17 : 9
Ratio of the surface area of Cylinder and cone = 17 : 9
Hence, the Ratio of the surface area of Cylinder and cone is 17 : 9
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