Question

the area of curved surface of a cylinder 4400 cm² and the circumference of its base is 110 cm . find the height of cylinder​

Answer 1

AnswEr :

$\textsf{We're given with the CSA of cylinder \textbf{that is 4400 \sf \: cm^2 .}} \\ \textsf{And it is also given the circumference of its base is \textbf{110 cm.}}$

$\rule{100}2$

• Let's Head to the Question Now :

$\underline{\bigstar\:\textsf{Circumference of its Base is 110 cm :}}$

$:\implies\sf 2\pi r = 110\\ \\ \footnotesize\sf{\quad {\bf}{\dag} \: Circumference= 2\pi r} \\\\:\implies\sf 2 \times \bigg(\dfrac{22}{7}\bigg) \times r = 110 \\\\\\:\implies\sf \dfrac{\cancel{44}}{7} \times r = \cancel{110}^{ \: \: \: \footnotesize{2.5}}\\\\\\:\implies{\boxed{\boxed{\sf{r = 17.5\;cm}}}}$

$\therefore{\underline{\textsf{Hence,\; radius\;of\; cylinder\;is\; \textbf{17.5 cm}.}}}$

$\rule{300}2$

$\underline{\bigstar\:\sf{Curved \;Surface \;Area\; is\; 4400 \;cm^2\; :}}$

$:\implies\sf 2 \pi r h = 4400 \\\\\footnotesize\sf{\quad {\bf}{\dag} \;CSA = 2\pi r h} \\\\:\implies\sf 2 \times \bigg(\dfrac{22}{7}\bigg) \times (17.5) \times h = 4400 \\\\\\:\implies\sf \dfrac{44}{7} \times (17.5) \times h = 4400 \\\\\\:\implies\sf \cancel\dfrac{770} {7}\times h = 4400 \\\\\\:\implies\sf 110 \times h = 4400 \\\\\\:\implies\sf h = \cancel\dfrac{4400}{110} \\\\\\:\implies{\underline{\boxed{\sf{h = 40\;cm}}}}$

$\therefore{\underline{\textsf{Hence,\;height\;of\; cylinder\;is\; \textbf{40 cm }.}}}$

Answer 2

Given

• Curved surface area of cylinder = 4400 cm
• Circumference of its base = 110 cm

To find

• Height of the cylinder

Solution

Circumference of its base = 100 cm

• 2π r = 110
• 2 × 22/7 × r = 110
• 44/7 × r = 110
• r = 110 × 7/44
• r = 17.5

Hence, the radius is 17.5 cm

Now,

Curved surface area = 4400

• 2πrh = 4400
• 2 × 22/7 × 17.5 × h = 4400
• 44/7 × 17.5 × h = 4400
• 110 × h = 4400
• h = 4400/100
• h = 40

Hence, the height of the cylinder is 40 cm

Verification

• Curved surface area = 4400
• 2πrh = 4400
• 2 × 22/7 × 17.5 × 40 = 4400
• 44/7 × 17.5 × 40 = 4400
• 110 × 40 = 4400
• 4400 = 4400
• L.H.S = R.H.S