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

Answer:

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 = $\frac{2}{3}$ of the total surface area

I.e The curved surface area of cylinder = $\frac{2}{3}$ × 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,  $(2\times \Pi \times r\times h) + (2\times \Pi\times r^{2} )$ = 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 + $(2\times \Pi\times r^{2} )$ = 21 cm  

Or,  $(2\times \Pi\times r^{2} )$ = 21 cm - 14 cm

Or, $(2\times \Pi\times r^{2} )$ = 7

so , r² = $\frac{7}{2\pi }$

∴    r² =  $\frac{49}{44}$

I.e  r = $\sqrt{\frac{49}{44} }$

So, radius = $\frac{7}{\sqrt{44} }$  cm

or,   r = 1.05 cm

Put the value of r in eq b

2 $\pi$ r h = 14 cm

Or,  2 $\pi$ ×  $\frac{7}{\sqrt{44} }$  × h = 14 cm

So, h = $\frac{\sqrt{44} }{\pi }$

Or, h = 2.11 cm

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