Question

find the height of the cylinder whose volume is 1.54 cubic m and radius of the base is 70 cm

Answer 1

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{ 70 \: cm}}\put(9,17.5){\sf{h}}\end{picture}$

Solution :

For a cylinder having a radius r and a height h ;

Volume Of Cylinder :

> π r² .

Here , the radius of the cylinder is given as 70 cm and the volume is 1.54 m³ .

Converting ;

1 m³ = 1 × 10⁶ cm³ .

> 1.54 × 10⁶ cm³ .

> 1540000 cm ³.

> π r² h = 1540000

> 22/7 × 70 × 70 × h = 1540000

> 22 × 10 × 70 h = 1540000

> 15400 h = 1540000

> h = 100 cm = 1 m.

This is the required answer .

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Answer 2

Answer:

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{ 70 \: cm}}\put(9,17.5){\sf{height (h)}}\end{picture}$

Given :-

• Volume = 1.54 m³
• Radius = 70 cm or

To Find :-

Height

Solution :-

1.54 m³ = 1540000

Now,

As we know that

$\boxed{ \rm \: Volume = \pi \: {r}^{2} h}$

1540000 = 22/7 × 70² × h

1540000 = 22/7 × 4900 × h

1540000 = 22 × 700 × h

1540000 = 154000

1540000/154000 = h

100 = h