Question

the total surface area of a solid cylinder is 21cm if the curved surface area of the solid cylinder is two - third of its total surface area find its radius and height​

Answer 1

The radius of cylinder is 1.05 cm and

The height of cylinder is 2.11 cm

Explanation:

Given as :

The total surface area of cylinder = 21 cm

The curved surface area of cylinder =
`(2)/(3)` of the total surface area

I.e The curved surface area of cylinder =
`(2)/(3)` × 21 = 14 cm

∵ The total surface area of cylinder = 2
`\pi` r h + 2
`\pi` r²

Where r is the radius and h is the height of cylinder

Or, 2
`\pi` r h + 2
`\pi` r² = 21 cm

Or,
`(2* \Pi * r* h) + (2* \Pi* r^(2) )` = 21 cm ....a

Again ∵ The curved surface area of cylinder = 2
`\pi` r h

Where r is the radius and h is the height of cylinder

Or, 2
`\pi` r h = 14 cm . ...b

so . put the value of a into b

I.e 14 cm +
`(2* \Pi* r^(2) )` = 21 cm

Or,
`(2* \Pi* r^(2) )` = 21 cm - 14 cm

Or,
`(2* \Pi* r^(2) )` = 7

so , r² =
`(7)/(2\pi )`

∴ r² =
`(49)/(44)`

I.e r =
`\sqrt{(49)/(44) }`

So, radius =
`(7)/(√(44) )` cm

or, r = 1.05 cm

Put the value of r in eq b

2
`\pi` r h = 14 cm

Or, 2
`\pi` ×
`(7)/(√(44) )` × h = 14 cm

So, h =
`(√(44) )/(\pi )`

Or, h = 2.11 cm

Hence The radius of cylinder is 1.05 cm and The height of cylinder is 2.11 cm Answer