# A solid cylinder has total surface area of 462 square centimeters its curved surface area is one third of its total surface area find the volume of the cylinder

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by piyanshu

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by piyanshu

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2(pi)R² + 2(pi)RH=462

2(pi)R² + 154=462

R²=308/2(pi)

R²=49

R=7

Since, 2(pi)RH=154

H=154/2(pi)R

H=7/2

Volume=(pi)R²H=539

= 1/3 TSA + 2πr²

TSA - 1/3 TSA = 2πr²

2/3 TSA = 2πr²

2/3 × 462 = 2πr²

r² = 49

r = 7

CSA = 154

2πrh = 154

2×22/7×7×h = 154

h = 154/44

h = 7/2

V = πr²h

= 22/7 × 7² × 7/2

=11 × 49

= 539 cm³

∴ the volume is 539 cm³

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