Question

The ratio between the Radius & height
of a cylinder 2.3 f its volume
is1617 cm cube find the Total Surface
area of the Cylinden.​

Answer 1

Given

Ratio of radius & height of cylinder = 2 : 3

Volume of cylinder = 1617 cm³

To find

Total surface area of cylinder

Solution

Let the radius & height of cylinder be 2n & 3n.

As we know,

➥ Volume of cylinder = πr²h

Putting values :

➝ 1617 = 22/7 × (2n)² × 3n

➝ 1617 = 22/7 × 4n² × 3n

➝ 1617 = 22/7 × 12n³

➝ 1617 × 7/22 = 12n³

➝ 11319/22 = 12n³

➝ 514.5 = 12n³

➝ n³ = 514.5/12

➝ n³ = 42.875

• Cubing root on both sides.

➝ ³√n = ³√42.875

➝ n = 3.5 cm

Now finding radius & height :

⟼ Radius of cylinder = 2n = 2(3.5) = 7 cm.

⟼ Height of cylinder = 3n = 3(3.5) = 10.5 cm

Now we know,

➥ TSA of cylinder = 2πr(r + h)

Putting values :

➻ TSA of cylinder = 2 × 22/7 × 7(7 + 10.5)

➻ TSA of cylinder = 2 × 22(17.5)

➻ TSA of cylinder = 44 × 17.5

➻ TSA of cylinder = 770 cm²

Therefore,

Total surface area of cylinder = 770 cm²

Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

The ratio between the Radius & height of a cylinder 2:3. If it's volume is 1617 cm³.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The total surface area of the cylinder.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the ratio be r

$\bf{We\:have}\begin{cases}\sf{Radius\:of\:cylinder\:(r)=2r}\\ \sf{Height\:of\:cylinder\:(h)=3r}\\ \sf{Volume\:of\:cylinder\:(V)=1617cm^{3} }\end{cases}}$

We know that formula of the volume of cylinder :

$\bf{\boxed{\bf{Volume\:of\:cylinder=\pi r^{2} h}}}}$

A/q

$\longrightarrow\sf{\pi (2r)^{2} \times 3r=1617}\\\\\longrightarrow\sf{\pi 4r^{2} \times 3r=1617}\\\\\longrightarrow\sf{\pi \times 12r^{3} =1617}\\\\\longrightarrow\sf{12r^{3} =\dfrac{1617}{\pi } }\\\\\longrightarrow\sf{r^{3} =\dfrac{1617\times 7}{22\times 12} \:\:[\pi =\frac{22}{7} ]}\\\\\\\longrightarrow\sf{r^{3} =\cancel{\dfrac{11319}{264} }}\\\\\\\longrightarrow\sf{r^{3} =\dfrac{343}{8} }\\\\\\\longrightarrow\sf{r=3\sqrt{\dfrac{343}{8} } }\\\\\\\longrightarrow\bf{r=\dfrac{7}{2} cm}}$

So;

$\bullet\sf{Radius=2r=\cancel{2}\times \dfrac{7}{\cancel{2}} }\\\\\bullet\sf{\green{Radius=7\:cm}}\\\\\bullet\sf{Height=3r=\cancel{3}\times \dfrac{7}{\cancel{2}} }\\\\\bullet\sf{\green{Height=\dfrac{21}{2} \:cm}}$

Now;

$\bf{\boxed{\bf{T.S.A\:of\:cylinder=2\pi r(h+r)\:\:\:\:(sq.unit)}}}}$

$\longrightarrow\sf{2\times \dfrac{22}{\cancel{7}} \times\cancel{ 7} \bigg(\dfrac{21}{2} +7\bigg)}\\\\\\\longrightarrow\sf{44\bigg(\dfrac{21+14}{2}\bigg)} \\\\\\\longrightarrow\sf{\cancel{44}\times \dfrac{35}{\cancel{2}} }\\\\\\\longrightarrow\sf{(22\times 35)cm^{2} }\\\\\\\longrightarrow\sf{\green{770\:cm^{2} }}$

Thus;

$\underbrace{\sf{The\:total\:surface\:area\:of\:the\:cylinder\:=770\:cm^{2} }}}}$