Question

Find The area of the tin sheet required to make a cylindrical container with its lid if it's radius of the base is 21 cm and the height is 28 cm also find the volume of the container​

Answer 1

★ AnswEr:-

• The area of the cylinder = 6468 cm^2
• The volume of the cylinder = 38808 cm^3

★ GivEn :-

• The radius of the base of the cylinder is 21 cm.
• The height of the cylinder is 28 cm.

★ To Find :-

• The area of the cylinder.
• The volume of the cylinder.

★ Diagram :-

$\setlength{\unitlength}{1.4cm} \thicklines \begin{picture}(2,0)\qbezier(0,0)(0,0)(0,2.5)\qbezier(2,0)(2,0)(2,2.5)\qbezier(0,0)(1,1)(2,0)\qbezier(0,0)( 1, - 1)(2,0) \put(1,1){\line(0,1){1}}\put(1,1){\line(0, - 1){1}}\put(1.1,1){ \bf 28 \: cm }\put(1.1,0.1){ \bf 21 \: cm }\put(1,0){\line(1,0){1}}\qbezier(0,2.5)(1,1.5)(2,2.5)\qbezier(0,2.5)(1, 3.5)(2,2.5){\boxed{ \bf @TheFairyTale }}\end{picture}$

★ Solution :-

The formula of the area of solid cylinder is,

$\implies \boxed{ \red{ \sf A_{cylinder } = 2\pi \times r(h + r)}}$

$\implies \sf A_{cylinder } = 2 \times \dfrac{22}{7} \times 21(28 + 21)$

$\implies \sf A_{cylinder } = 2 \times \dfrac{22}{7} \times 21 \times 49$

$\implies \sf A_{cylinder } = 2 \times 22 \times 21 \times 7$

$\implies \boxed { \red{\sf A_{cylinder } = 6468 \: {cm}^{2} }}$

We know the formula of volume of cylinder,

$\implies \boxed{ \red{ \sf V_{cylinder } = \pi \times {r}^{2} \times h }}$

$\implies \: \dfrac{22}{7} \times 21 \times 21 \times 28$

$\implies \: 22 \times 21 \times 21 \times \: 4$

$\implies \boxed{ \red{ \sf V_{cylinder } = 38808 \: {cm}^{3} }}$