Question

★ Maths Problem !!

1: Given that the base radius of a cylinder is half its height . If the C.S.A of the cylinder is 616 m². Find the Volume of the Cylinder.

→ Solve without spamming !
→ Surprise for quality answerers
​​

Answer 1

Answer:

2156 m³

Step-by-step explanation:

Given -

Curved Surface Area of cylinder = 616 m²

Base radius of cylinder (r) = half of height of cylinder (h)

To find -

Volme of cylinder

Solution -

To find the volume, we have to find the radius and height of the cylinder

given that radius = 1/2 height

if we consider height as 2x then radius will be 1/2 of x = x.

CSA = 2πrh

CSA = 616 m²

=> 2πrh = 616 m²

=> 2×22/7 × 2x × x = 616

=> 44/7 × 2x² = 616

=> 88x²/7 = 616

=> 88x² = 616×7

=> 88x² = 4312

=> x² = 4312/88

=> x² = 49

=> x = √49

=> x = 7

means radius = 7 m

height = 2x = 14 m

volume = πr²h

= 22/7 × 7×7×14

= 22×7×14×7/7

= 22×7×14

= 2156 m³

Hence volume = 2156 m³.

hope it helps.

Answer 2

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt 1:\: Given\: that\: the\: base\: radius\: of\: a\: cylinder\: is\: half\\\tt its\: height.\:If\: the\: C.S.A \:of\: the\: cylinder\: is \:616 \:{m}^{2}.\\\tt Find\: the\: Volume\: of \:the\: Cylinder.$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\bf The\: base\: radius\: of\: a\: cylinder\: is\: half\:its\: height$

${\sf {\longrightarrow {r=\dfrac{1}{2}\times h}}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: { \boxed {\sf {{h=2r}}}}$

• $\bf C.S.A\:of\:cylinder =616\:{m}^{2}$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• $\bf Volume \:of\:the \:cylinder$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\pink {\underline {\bf {\pmb {Radius \:of \:the \:cylinder}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {C.S.A_{(Cylinder)}=2\pi rh}}}}}}}$

• $\sf C.S.A=curved \:surface \:area\:of\:the\:cylinder$
• $\sf r=radius \:of\:the\:cylinder$
• $\sf h=height \:of\:the\:cylinder$

${\underbrace {\overbrace {\orange{\pmb {Substitute \:the \:values}}}}}$

$\bf \implies 616=2 \times \dfrac{22}{7}\times r \times 2r$

$\bf \implies 616=\dfrac{44}{7} \times 2{r}^{2}$

$\bf \implies 616=\dfrac{88{r}^{2}}{7}$

$\bf \implies 616\times 7=88{r}^{2}$

$\bf \implies 4312=88{r}^{2}$

$\bf \implies {r}^{2}=\dfrac{4312}{88}$

$\bf \implies {r}^{2}=\dfrac{\cancel{4312}}{\cancel{88}}$

$\bf \implies {r}^{2}=49$

$\bf \implies r=\sqrt{49}$

$\implies {\blue {\boxed {\boxed {\purple {\sf {r=7\:m}}}}}}$

——————————————————————————————

${\pink {\underline {\bf {\pmb {Height\:of \:the \:cylinder}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {h=2r \longrightarrow(Given) }}}}}}}$

• $\sf h=height \:of \:the \:cylinder$
• $\sf r=radius \:of\:the\:cylinder$

${\underbrace {\overbrace {\orange{\pmb {Substitute \:the \:values}}}}}$

$\bf \implies h=2\times 7$

$\implies {\blue {\boxed {\boxed {\purple {\sf {h=14\:m}}}}}}$

——————————————————————————————

${\pink {\underline {\bf {\pmb {Volume\:of \:the \:cylinder}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {V_{(Cylinder)}=\pi{r}^{2}h}}}}}}}$

• $\sf V=volume \:of\:the \:cylinder$
• $\sf r=radius \:of\:the\:cylinder$
• $\sf h=height \:of\:the\:cylinder$

${\underbrace {\overbrace {\orange{\pmb {Substitute \:the \:values}}}}}$

$\bf \implies V=\dfrac{22}{7}\times {\big(7\big)}^{2}\times 14$

$\bf \implies V=\dfrac{22}{7}\times 7 \times 7\times 14$

$\bf \implies V=\dfrac{22}{\cancel{7}}\times \cancel{7} \times 7\times 14$

$\bf \implies V=22 \times 7 \times 14$

$\bf \implies V=22\times 98$

$\implies {\blue {\boxed {\boxed {\purple {\mathfrak {V=2156\:{m}^{3}}}}}}}$

______________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf Curved \:surface \:area \:of \:the \:cylinder =2\pi rh$

$\sf Total \:surface \:area \:of \:the \:cylinder =2\pi r(r+h)$

$\sf Volume \:of \:the \:cylinder =\pi{r}^{2}h$