Question

The curved surface area of a cylinder is 7920 cm2 and the circumference of the base of the base is 126 cm. Find the height of the cylinder

Answer 1

$\sf Given \begin{cases} & \sf{Curved\:surface\:area = \bf{7920\:cm^2}} \\ & \sf{Circumference\:of\:base = \bf{126\:cm}} \end{cases}$

To find: Height of the cylinder?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀

☯ Let height of cylinder be h cm.

⠀⠀⠀⠀

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

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

$:\implies\sf 2 \times \dfrac{22}{7} \times r = 126$

$:\implies\sf \dfrac{44}{7} \times r = 126$

$:\implies\sf r = \cancel{126} \times \dfrac{7}{ \cancel{44}}$

$:\implies\sf r = 2.87 \times 7$

$:\implies{\underline{\boxed{\frak{\purple{r = 20.09\:cm\:\:(approx)}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Radius\:of\:cylinder\:is\: {\textsf{\textbf{20.09\:cm}}}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀

Now Given that,

⠀⠀⠀⠀

• Curved surface area of cylinder = 7920 cm²

⠀⠀⠀⠀

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

$:\implies\sf 2 \times \dfrac{22}{7} \times 20.09 \times h = 7920$

$:\implies\sf \dfrac{44}{7} \times 20.09 \times h = 7920$

$:\implies\sf 20.09 \times h = \cancel{7920} \times \dfrac{7}{ \cancel{44}}$

$:\implies\sf 20.09 \times h = 180 \times 7$

$:\implies\sf 20.09 \times h = 1260$

$:\implies\sf h = \cancel{ \dfrac{1260}{20.09}}$

$:\implies{\underline{\boxed{\frak{\purple{h = 62.8\:\:(approx)}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Height\:of\:cylinder\:is\: {\textsf{\textbf{62.8\:cm}}}.}}}$

Answer 2

Answer:

Given :-

• The curved surface area of a cylinder is 7920 cm² and the circumference of the base is 126 cm.

To Find :-

• What is the height of the cylinder.

Formula Used :-

$\boxed{\bold{\large{Circumference\: of\: a\: circle\: =\: 2{\pi}r}}}$

$\boxed{\bold{\large{C.S.A\: of\: a\: cylinder\: =\: 2{\pi}rh}}}$

Solution :-

Given :

• C.S.A of a cylinder = 7920 cm²
• Circumference of a base = 126 cm

First, we have to find the radius,

According to the question by using the formula we get,

⇒ $\sf126\: =\: 2 \times \dfrac{22}{7} \times r$

⇒ $\sf126\: =\: \dfrac{44}{7} \times r$

⇒ $\sf{\cancel{126}}\: \times \dfrac{7}{\cancel{44}} =\: r$

⇒ $\sf2.87 \times 7 =\: r$

⇒ $\sf20.09 (approx) =\: r$

➠ $\small\bf{\underbrace{\red{r\: =\: 20.09}}}$

Hence, the radius of a cylinder is 20.09 cm .

Now, we have to find the height of a cylinder,

Given :

• Radius of a cylinder = 20.09 cm
• C.S.A of a cylinder = 7920 cm²

According to the question by using the formula we get,

↦ $\sf7920\: =\: 2 \times \dfrac{22}{7} \times 20.09 \times h$

↦ $\sf7920\: =\: \dfrac{44}{7} \times 20.09 \times h$

↦ $\sf{\cancel{7920}}\: \times \dfrac{7}{\cancel{44}} = 20.09 \times h$

↦ $\sf1260\: =\: 20.09 \times h$

↦ $\sf\dfrac{\cancel{1260}}{\cancel{20.09}} =\: h$

↦ $\sf62.8 (approx) =\: h$

➦ $\small\bf{\underbrace{\red{h\: =\: 62.8}}}$

$\therefore$ The height of a cylinder is 62.8 cm .