Question

if the height of cylinder is 21cm and it's volume and curved surface area are equal, what will be it's total surface area?​

Answer 1

Given :-

CSA OF CYLINDER = VOLUME OF CYLINDER

2πRH = πR²H

2R = R²

2 = R

TSA OF CYLINDER = 2πR ( R + H )

= 2 * 22/7 * 2 ( 2 + 21 )

= 88/7 ( 23 )

= 2024 / 7

The TSA OF CYLINDER is 2024/7 or 289.14 cm²

Answer 2

Answer:

Given:-

• Height of cylinder= 21m
• Volume of cylinder = CSA of cylinder

To Find:-

• TSA of cylinder

$\sf \large \underline{Step \: \: 1}$

Since it is given that,

$\sf \rightarrow{ Volume \: \: of \: \: cylinder = CSA \: \: of \: \: cylinder}$

$\sf \large \rightarrow \pi {r}^{2} h = 2\pi rh$

$\sf \large \rightarrow \frac{\pi {r}^{2} h}{\pi rh} = 2$

$\sf \rightarrow \red{r = 2}$

$\sf \large \underline{Step \: 2}$

Now We find the TSA of cylinder

$\sf \large\rightarrow{TSA \: \: of \: \: cylinder = 2\pi r(r + h)}$

Now put the values in above formula

$\sf \large \rightarrow{TSA =2 \times \frac{22}{7} \times 2 (2 + 21)}$

$\sf \large \rightarrow{TSA = 2 \times \frac{22}{7} \times 2 \times 23}$

$\sf {\boxed {\red{ \sf</strong><strong>{TSA =289.14 \: {cm}^{2} }}}</strong><strong>}</strong><strong>$