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Mathematics

The sum of the height and the radius of a solid cylinder is 35 cm and its total surface area is 3080 cm2; find the volume of the cylinder.

Mensuration

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Answer

According to question,

h + r = 35 ………(1)

Total surface area = 3080

⇒ 2πr(h + r) = 3080

⇒ 2πr × 35 = 3080

⇒ 70×227×r70 \times \dfrac{22}{7} \times r = 3080

⇒ 220r = 3080

⇒ r = 3080220\dfrac{3080}{220}

⇒ r = 14 cm.

⇒ h + r = 35

⇒ h + 14 = 35

⇒ h = 35 - 14

⇒ h = 21 cm.

Volume of cylinder = πr2h

= 227×(14)2×21\dfrac{22}{7} \times (14)^2 \times 21

= 22 × 2 × 14 × 21

= 12936 cm3.

Hence, volume of cylinder = 12936 cm3.

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