The radius and the height of a cylinder are in the ratio 2:3. If its volumeis 54πr find its csa in terms of π.
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Answer:
given r : h = 2 : 3
r = 2x and h = 3x
volume V = pi*r²*h
V = pi*(2x)²*(3x)
=> 54*pi*r = pi*4x²*3x
=> 54*pi*2x = pi*12x³
=> 54*2 = 12*x² [ pi and one x cancels out ]
=> 54 = 6x²
=> 9 = x²
=> x = √9 = 3
therefore r = 2x = 2×3 = 6 cm
h = 3x = 3×3 = 9 cm
CSA = 2*pi*r*h
=> 2*π*6*9
=> 108 π
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