a right circular cylinder and a cone have equal bases and equal Heights if their curved surface area are in ratio 8 : 5 so that the ratio between radius of the base to their height is 3:4
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Let r be the radius of cone and cylinder and h be their height.
ATQ,
C. S. A of cylinder / C. S. A of cone = 8/5
2πrh/πrl = 8/5 ( πr cancel from numerator and denominator)
Now, l = √(h²+r²)
Therefore,
2h /√h²+r²=8/5
By transportation of values
10h = 8√(h²+r²)
Squaring both sides,
100h² = 64 h² + 64 r²
36 h²=64 r²
Therefore,
h²/r² = 64/36
Square root both sides
h / r = 8/6
h/r = 4/3
=>r/h=3/4
ATQ,
C. S. A of cylinder / C. S. A of cone = 8/5
2πrh/πrl = 8/5 ( πr cancel from numerator and denominator)
Now, l = √(h²+r²)
Therefore,
2h /√h²+r²=8/5
By transportation of values
10h = 8√(h²+r²)
Squaring both sides,
100h² = 64 h² + 64 r²
36 h²=64 r²
Therefore,
h²/r² = 64/36
Square root both sides
h / r = 8/6
h/r = 4/3
=>r/h=3/4
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