Question

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Answer 1

QUESTION:

❍ The curved surface area of a cylinder is 264 cm² and circumference of the base 44 cm. Find the height of the cylinder.

• 6 cm
• 5 cm
• 8 cm
• 4 cm

★ ANSWER ★

• 6 cm (✔)

GIVEN:

Let the radius of the cylinder be 'r' cm

✎ The circumference of the base of the cylinder is 44 cm

To find the circumference, we use the formula:-

❰ CIRCUMFERENCE = 2πr ❱

According to question:-

➜ 44 = 2 $\times$ $\sf{\dfrac{22}{7}}$ $\times$ r

➜ 44 = $\sf{\dfrac{44}{7}}$ $\times$ r

➜ 44 $\times$ 7 = 44 $\times$ r

➜ $\sf{\cancel\dfrac{308}{44}}$ = r

❬ r = 7 cm ❭

Let the height of the cylinder be 'h' cm

We know that, the formula for finding the CSA of Cylinder is:-

❰ C.S.A = 2πrh ❱

On putting the values in the formula, we get

➜ 264 = 2 $\times$ $\sf{\dfrac{22}{7}}$ $\times$ 7 $\times$ h

➜ 264 = 2 $\times$ 22 $\times$ h

➜ 264 = 44 $\times$ h

➜ $\sf{\cancel\dfrac{264}{44}}$ = h

❬ h = 6 cm ❭

❝ Hence, the height of the cylinder is 6 cm ❞

______________________

Answer 2

★ Given : The curved surface area of a cylinder is 264 cm² and circumference of the base 44 cm.

$\rule{130}1$

★ Solution :

Let the radius of cylinder be r cm.

☯ $\underline{\boldsymbol{According\:to \: Question :}}$

$\dashrightarrow{\boxed{\boxed{\bf\:\: Circumference \:of\: cylinder= 2\pi r}}}\\\\\\\dashrightarrow\sf\:\: 44 = 2 \times \dfrac{22}{7} \times r\\\\\\\dashrightarrow\sf\:\: 44 = \dfrac{44}{7}\times r\\\\\\\dashrightarrow\sf\:\: 44 \times 7 = 44 \times r\\\\\\\dashrightarrow\sf\:\: 308 = 44 \times r\\\\\\\dashrightarrow\sf\:\: r = \dfrac{308}{44} \\\\\\ \dashrightarrow\:\:\underline{\boxed{\textbf {r = 7 \:cm}}}\:\bigstar$

$\therefore\:\underline{\textsf{Radius of the cylinder is \textbf{7 cm}}}.$

$\rule{150}1$

Let the height of the cylinder be h cm.

$:\implies{\boxed{\boxed{\bf CSA \:of\: cylinder = 2\pi rh}}} \\\\\\:\implies\sf 264 = 2 \times \dfrac{22}{7} \times 7 \times h\\\\\\:\implies\sf 264 = 2 \times 22 \times h\\\\\\:\implies\sf h = \dfrac{264}{44}\\\\\\:\implies\:\:\underline{\boxed{\textbf { h = 6 cm}}}\:\bigstar$

⠀

$\therefore\:\underline{\textsf{Height of the cylinder is \textbf{6 cm}}}.$

$\rule{170}2$

$\boxed{\begin{minipage}{6.5 cm}\underline{\textsf{\dag \:Some Important Formulae Related to it :}}\\ \\ \bullet\tt Volume = \pi r^2 h\\ \\\bullet\tt Surface\: area = 2 \pi rh + 2 \pi r^2\\ \\\bullet\tt Lateral \:area = 2 \pi rh \\ \\\bullet\tt Base \:area = \pi r^2\end{minipage}}$