Question

The volume of a right circular cylinder is 1100cm3 and the radius of its
base is 5cm. Find the curved surface area.

Answer 1

$\frak{Given}\begin{cases}\sf{\;\;\; Volume_{\:(cylinder)} = 1100\;cm^3}\\\sf{\:\;\; Radius = 5 cm}\end{cases}$

Need to find: The Curved surface area of the cylinder.⠀

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

⠀⠀

$\star\;{\boxed{\sf{\pink{Volume_{\;(cylinder)} = \pi r^2 h}}}}$

where,

⠀⠀

• r & h are radius and height of cylinder respectively. And, volume is given 1100 cm³. Comparing,

$:\implies\sf \pi r^2 h = 1100 \\\\\\:\implies\sf h = \dfrac{1100}{\dfrac{22}{7} \: \times (5)^2} \\\\\\:\implies\sf h = \dfrac{\cancel{1100}\; \times 7}{\cancel{22}\; \times\; \cancel{25}}\\\\\\:\implies\sf h = 2 \times 7\\\\\\:\implies{\underline{\boxed{\sf{h = 14\;cm}}}}$

⠀⠀

$\therefore{\underline{\sf{Hence,\; Height\; of \; cylinder \; is\; \bf{14\:cm }.}}}$

⠀⠀

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

Now,

⠀⠀

$\star\;{\boxed{\sf{\pink{CSA_{\;(cylinder)} = 2 \pi r h}}}}$

⠀⠀

Therefore,

⠀⠀

$:\implies\sf CSA_{\:(cylinder)} = 2 \times \dfrac{22}{\cancel{7}} \; \times 5 \times \:\cancel{14} \\\\\\:\implies\sf CSA_{\:(cylinder)} = 2 \times 22 \times 10\\\\\\:\implies\sf CSA_{\:(cylinder)} = 44 \times 10\\\\\\:\implies{\underline{\boxed{\sf{\purple{CSA_{\:(cylinder)} = 440\;cm^2}}}}}\;\bigstar$

⠀⠀

$\therefore{\underline{\sf{Hence, \:CSA \; of \; cylinder\; is\; \bf{440\;cm^2 }.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:Formula\:Related\:to\:cylinder\:\bigstar}}}}$

• $\sf Area\:of\:base\:of\:cylinder = \bf{\pi r^2}$

• $\sf Total\:Surface\:area\:of\:cylinder = \bf{2 \pi r(r + h)}$

• $\sf Curved\:Surface\:area\:of\:cylinder = \bf{2 \pi rh}$

• $\sf Volume\; of \; cylinder = \bf{\pi r^2 h}$

Answer 2

☆Answer☆

Given:-

• Volume of right circular cylinder = 1100 cm³
• It's Base Radius = 5 cm

Solution:-

Volume of right circular cylinder = 1100 cm³

πr²h = 1100 cm³

22/7 × 25 × h = 1100 cm³

h = (1100×7)/(25×22)

h = 14 cm

Now,

Curved surface area of cylinder = 2πrh

=> 2×(22/7)×5×14

=> 440 cm²

Thus, curved surface area of right circular cylinder is 440 cm².

✔