Question

Find the total surface area of ​​the sheet required for a closed balance of radius 4.2 cm and height 6 cm. Also find the volume of this cylinder​

Answer 1

Correct Question:

Find the total surface area of the sheet required to make a closed cylinder of radius 4.2 cm and height 6 cm. Also find the volume of this cylinder.

Given Information: The Radius of Closed cylinder is 4.2cm and it's Height is 6cm.

Need to Find: The Total surface area of Cylinder and The volume of Cylinder

Formula Used: $\\\hookrightarrow\tt{Total\: surface\: area\: of\: Cylinder=2\times \pi\times r(h+r)}$

$\hookrightarrow\tt{Volume\: of\: Cylinder=\pi\times {r}^{2}\times h}$

Where,

• r is Radius of Cylinder
• h is Height of Cylinder

________________________________

Solution:

$\longmapsto\sf{Radius\: of\: Cylinder=r=4.2\: cm}$

$\longmapsto\sf{Height\: of\: Cylinder=h=6\: cm}$

~Substituting all the values in Formula,

$\\ \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \sf{Total\: surface\: area\: of\: Cylinder=2\times \pi\times r(h+r)}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \sf{Total\: surface\: area\: of\: Cylinder=2\times \dfrac{22}{7}\times 4.2(6+4.2)}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \sf{Total\: surface\: area\: of\: Cylinder=2\times \dfrac{22}{7}\times 4.2(10.2)}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \sf{Total\: surface\: area\: of\: Cylinder=2\times \dfrac{22}{7}\times 42.84}$

$\\ \: \: \: \: \: \: \: \: \: \: \:\longrightarrow \sf{Total\: surface\: area\: of\: Cylinder=\dfrac{22}{7}\times 85.68}$

$\\ \: \: \: \: \: \: \: \: \: \: \:\longrightarrow \bold{Total\: surface\: area\: of\: Cylinder=\color{red}{269.28\: {cm}^{2}}}$

• Henceforth, the Total Surface area of Cylinder is 26.28cm²

Now,

$\\ \: \: \: \: \: \: \: \: \: \: \: \implies \sf{Volume\: of\: Cylinder=\pi\times {r}^{2}\times h}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \implies \sf{Volume\: of\: Cylinder=\dfrac{22}{7}\times {4.2}^{2}\times 6}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \implies \sf{Volume\: of\: Cylinder=\dfrac{22}{7}\times 17.64\times 6}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \implies \sf{Volume\: of\: Cylinder=\dfrac{22}{7}\times 105.84}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \implies \bold{Volume\: of\: Cylinder=\color{red}{332.64\: {cm}^{3}}}$

Required Answer:

$\twoheadrightarrow$ Total Surface Area of Cylinder is $\bold\color{purple}{26.28\: {cm}^{2}}$

$\twoheadrightarrow$ Volume of Cylinder is $\bold\color{purple}{332.64\: {cm}^{3}}$