Question

the ratio of radius of base to the height of a right circular cylinder is 1 is to 2 if its volume is 2156 then its total surface area is​

Answer 1

Answer:

Total surface area= 925 cm^2

Answer 2

correct question :

→ The ratio between the radius of the base and height of a cylinder is 1:2. If it's volume is 2156 ${cm}^3$. Find the total surface area of cylinder.

$\textbf{\underline{\underline{Step-By-Step\: Explanation}}}$  

Let radius of base of the given cylinder be ' r ' cm and height be ' h ' cm.

$\dfrac{r}{h}$ = $\dfrac{1}{2}$

⇒ r = $\dfrac{1}{2}$ × h

∵ Volume of cylinder = πr²h

2156 = $\dfrac{22}{7}$ × $\dfrac{1}{2} h$ × $\dfrac{1}{2}h$ ×h

⇒ 2156 = $\dfrac{22}{7}$ × $\dfrac{1}{4}$ h³

⇒ h³ = $\dfrac{2156×7×4}{22}$

⇒ h³ = 2744

⇒ h = ∛2744

⇒ h = 14 cm

∴ height of the given cylinder is 14 cm.

Radius = $\dfrac{1}{2}$ h

           = $\dfrac{1}{2}$ × h = 7 cm

∴ Radius of the given cylinder is 7 cm.

Now,

Total surface Area of cylinder = 2πr(r+h)

= 2 × $\dfrac{22}{7}$ × 7 ( 7 + 4 )

= 2 × 22  × 21

= 924 cm²

Therefore,

Total surface area of the given cylinder is 924 cm³

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