Question

Find the height of the cylinder whose volume is 1.54m³ and diameter of the base 140cm.

Answer 1

Given:

1. Volume = 1.54 ${m}^{3}$
2. Diameter of base = 140cm

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Need to find:

• Height =?

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Solution:

Diameter = Radius × 2

→ Radius = Diameter ÷ 2

→ Radius = 140 cm ÷ 2

→ Radius = 70 cm

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1 m³ = 1000000m³

→ 1.54${m}^{3} =$ 1540000 cm³

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We know,

Volume of a cylinder = $\pi {r}^{2} h$

→ Volume = $\pi \times {70}^{2} \times h$

→ 1540000 = $\dfrac{22}{7} \times 70 \times 70 \times h$

→ 1540000 = $22 \times 10 \times 70 \times h$

→ h = $\dfrac{1540000}{22 \times 700}$

→$\red{\bold{\boxed{\large{h = 100cm}}}}$

Height of cylinder is 100cm.

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

Answer 2

We have :

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• Volume = 1.54m³
• Diameter of the base = 140cm
• Radius = $\sf{\dfrac{140}{2}=70cm=0.7m}$

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To find :

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• The height of the cylinder

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Solution :

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Let the height of the cylinder be h.

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∵ Volume of cylinder = πr²h

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$\sf{\implies{\pi r^2 h=1.54}}$

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$\sf{\implies{\dfrac{22}{7}×0.7×0.7×h=1.54}}$

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$\sf{\implies{h=\dfrac{1.54×7}{22×0.7×0.7}}}$

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${\implies{\underline{\boxed{\pink{\sf{h={\frak{1\:{\sf{m}}}}}}}}}}{\:\star}$

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∴ The height of the cylinder is 1m.