Question

The curved surface area of a right circular of height 14cm is 88cm². Find diameter of the base of the cylinder​

Answer 1

$\sf Given \begin{cases} & \sf{CSA\:of\:cylinder = \bf{88\:cm^2}} \\ & \sf{Height\:of\:cylinder,\:h = \bf{14\:cm}} \end{cases}$

To find: Diameter of the base of cylinder?

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☯ Let's consider the radius of right circular cylinder be r cm.

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Curved\:Surface\:Area_{\;(cylinder)} = 2 \pi rh}}}}$

$:\implies\sf 88 = 2 \times \dfrac{22}{7} \times r \times 14\\ \\ \\ :\implies\sf 88 = \dfrac{44}{ \cancel{7}} \times r \times \cancel{14}\\ \\ \\ :\implies\sf 88 = 44 \times r \times 2\\ \\ \\ :\implies\sf r = \dfrac{88}{44 \times 2}\\ \\ \\ :\implies\sf r = \cancel{\dfrac{88}{88}}\\ \\ \\:\implies{\underline{\boxed{\frak{\purple{r = 1\:cm}}}}}\;\bigstar$

As we know that,

Diameter is double of Radius. So,

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$:\implies\sf Diameter = 2 \times 1\:cm\\ \\ \\ :\implies\sf Diameter = \bf{2\:cm}$

$\therefore\:{\underline{\sf{Diameter\:of\:right\: circular\:cylinder\:is\: {\textsf{\textbf{2\:cm}}}.}}}$

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$\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

$\boxed{\begin{minipage}{6.2 cm}\bigstar \:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}$

Answer 2

Answer:

Given :-

• Height of cylinder = 14 cm
• CSA of cylinder = 88 cm²

To Find :-

Diameter

Solution :-

As we know that

$\frak \red{{CSA = 2\pi} rh}$

Here,

R is the Radius

H is the Height

π is the 22/7

$\tt \implies \: 88 = 2 \times \dfrac{22}{7} \times r \times 14$

$\tt \implies \: 88 = 2 \times 22 \times r \times 2$

$\tt \implies \: 88 = 88r$

$\tt \implies \: r = \cancel \dfrac{88}{88}$

$\tt \implies \: r = 1 \: cm$

Now,

Let's find Diameter

$\frak \blue{Diameter \: = Radius \times 2}$

$\tt \implies \: Diameter = 1 \times 2$

${\frak {Diameter = 2 \: cm}}$

Hence :-

Diameter of its base is 2 cm.

Learn More :-

Area of square = πr²

Circumference of circle = 2πr