Question

Q10) if the circumference of the base of cylinder is
44cm and the sum of its radius and height is
27 cm, find its total surface area.

____________________

Don't spam :)
_____________________​

Answer 1

Answer:

Given:-

Area of trapezium shaped field is 600m².

• Height of trapezium is 24 m.
• Length of one of its parallel side is 20 m.

To Find:-

Length of the other parallel side.

Solution:-

Here, Area of Trapezium = $\dfrac{1}{2}\times height \times ( sum\ of \ parallel \ sides)$

Let the another parallel side be x m.

So, Putting values we get,

⇒ 600 m² =  $\dfrac{1}{2}\times 24 \ m \times ( 20 \ m + x \ m )$

⇒ $\dfrac{600 \ m^{2} \times 2}{24 \ m} = ( 20 \ m + x \ m )$

⇒ $50 \ m - 20 \ m = x$

⇒ $x = 30 \ m$

Hence, Other parallel side of trapezium is 30 m.

Some Important Terms:-

Area of Triangle = $\dfrac{1}{2}\times base \times height$

Area of square = $Side^{2}$

Area of Rectangle = $Length \times Breadth$

Answer 2

$\huge\sf \pmb{\orange {\underline \pink{\underline{\:Ꭺ ꪀ \mathfrak ꕶ᭙ꫀя \: }}}}$

$[tex]\sf Given \begin{cases} & \sf{Circumference\:of\:the\:base\;of\:cylinder = \bf{44\:cm}} \\ & \sf{Sum\:of\:radius\:and\:height\:of\:cylinder = \bf{27\:cm}} \end{cases}$

To find: Total surface area of cylinder?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀

☯ Let's consider r and h be the radius and height of cylinder respectively.

⠀⠀⠀⠀

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

$\star\;{\boxed{\sf{\pink{Circumference_{\;(circle)} = 2 \pi r}}}}$

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

$:\implies\sf \dfrac{44}{7} \times r = 44$

$:\implies\sf r = \cancel{44} \times \dfrac{7}{ \cancel{44}}$

$:\implies{\underline{\boxed{\frak{\purple{r = 7\:cm}}}}}\;\bigstar$

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

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

Sum of radius and height of cylinder is 27 cm.

⠀⠀⠀⠀

$:\implies\sf r + h = 27$

$:\implies\sf 7 + h = 27$

$:\implies\sf h = 27 - 7$

$:\implies{\underline{\boxed{\frak{\purple{h = 20\:cm}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Height\:of\:cylinder\:is\: {\textsf{\textbf{20\:cm}}}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

☯ Now, Finding Curved surface area of cylinder,

⠀⠀⠀

$\star\;{\boxed{\sf{\pink{Total\:surface\:area_{\;(rectangle)} = 2 \pi r(r + h)}}}}$

$:\implies\sf 2 \times \dfrac{22}{ \cancel{7}} \times \cancel{7} \bigg( 7 + 20 \bigg)$

$:\implies\sf 2 \times 22 \times 27$

$:\implies{\underline{\boxed{\frak{\purple{1188\:cm^2}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Total\:surface\:area\:of\:cylinder\:is\: \bf{1188\:cm^2}.}}}$