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

The radius of cylinder is 1.05 cm and

The height of cylinder is 2.11 cm

Step-by-step explanation:

Given as :

The total surface area of cylinder = 21 cm

The curved surface area of cylinder = of the total surface area

I.e The curved surface area of cylinder = × 21 = 14 cm

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

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

Or, 2 r h + 2 r² = 21 cm

Or,   = 21 cm   ....a

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

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

Or, 2 r h = 14 cm    . ...b

so . put the value of a into b

I.e 14 cm + = 21 cm  

Or,   = 21 cm - 14 cm

Or, = 7

so , r² =

∴    r² =  

I.e  r =

So, radius =  cm

or,   r = 1.05 cm

Put the value of r in eq b

2 r h = 14 cm

Or,  2 ×    × h = 14 cm

So, h =

Or, h = 2.11 cm

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

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step-by-step explanation: