Question

the curved surface area of cylindrical pillar is 264 and volume is 924 find the radius and height​

Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ CSA of the cylinder is 264

✭ Volume of the cylinder is 924

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ The Radius and the height?

$\displaystyle\large\underline{\sf\gray{Solution}}$

CSA of a cylinder is given by,

$\displaystyle\underline{\boxed{\sf CSA_{cylinder} = 2\pi rh }}$

Volume of the cylinder is given by,

$\displaystyle\underline{\boxed{\sf Volume_{cylinder} = \pi r^2h}}$

━━━━━━━━━

$\underline{\bigstar\:\textsf{According to the given Question :}}$

➝ $\displaystyle\sf CSA_{cylinder} = 2\pi rh$

➝ $\displaystyle\sf 264 = 2\times\dfrac{22}{7}\times r\times h$

➝ $\displaystyle\sf \dfrac{264 \times 7}{44} = r\times h$

➝ $\displaystyle\sf \dfrac{1848}{44} = r\times h$

➝ $\displaystyle\sf 42 = r\times h$

➝ $\displaystyle\sf h = \dfrac{42}{r}\:\:\:-eq(1)$

So then,

»» $\displaystyle\sf Volume_{cylinder} = \pi r^2h$

»» $\displaystyle\sf 924 = \dfrac{22}{7} \times r^2\times \dfrac{42}{r}$

»» $\displaystyle\sf 924 = \dfrac{22}{7} \times r\times 42$

»» $\displaystyle\sf 924\times 7 = 924r$

»» $\displaystyle\sf 6468 = 924r$

»» $\displaystyle\sf \dfrac{6468}{924} = r$

»» $\displaystyle\sf\orange{Radius = 7}$

From eq(1)

➳ $\displaystyle\sf h = \dfrac{42}{r}$

➳ $\displaystyle\sf h = \dfrac{42}{7}$

➳ $\displaystyle\sf\pink{Height = 6}$

$\displaystyle\therefore\:\underline{\sf The \ height \ is \ 6 \ \& \ radius \ is \ 7}$

━━━━━━━━━━━━━━━━━━