r = d/2

= 140/2 = 70 cm = 0.7 m

Volume of cylinder = πr²h

154 = 3.14 × 0.7²× h

h = 154/3.14× 0.49

h = 100m

Verified answer

Answer:

Given :-

• A cylinder whose volume is 1.54 m³ and diameter of the base is 140 cm.

To Find :-

• What is the height of the cylinder.

Solution :-

First, we have to find the radius of a cylinder :

Given :

• Diameter = 140 cm

According to the question by using the formula we get,

[tex]\implies \sf\boxed{\bold{Radius =\: \dfrac{Radius}{2}}}\\[/tex]

[tex]\implies \sf Radius =\: \dfrac{140}{2}\\[/tex]

[tex]\implies \bf Radius =\: 70\: cm\\[/tex]

Let's convert the radius of a cylinder cm into m :

[tex]\implies \sf Radius =\: 70\: cm\\[/tex]

[tex]\implies \sf Radius =\: \dfrac{70}{100}\: m\\[/tex]

[tex]\implies \sf\bold{Radius =\: 0.7\: m}\\[/tex]

Now, we have to find the height of the cylinder :

Given :

• Volume = 1.54 m³
• Radius = 0.7 m

According to the question by using the formula we get,

[tex]\implies \sf\boxed{\bold{Volume_{(Cylinder)} =\: {\pi}r^2h}}\\[/tex]

[tex]\implies \sf 1.54 =\: \dfrac{22}{7} \times (0.7)^2 \times h\\[/tex]

[tex]\implies \sf 1.54 =\: \dfrac{22}{7} \times (0.7 \times 0.7) \times h\\[/tex]

[tex]\implies \sf 1.54 =\: \dfrac{22}{7} \times 0.49 \times h\\[/tex]

[tex]\implies \sf 1.54 =\: \dfrac{22 \times 0.49}{7} \times h\\[/tex]

[tex]\implies \sf 1.54 =\: \dfrac{10.78}{7} \times h\\[/tex]

[tex]\implies \sf 1.54 \times \dfrac{7}{10.78} =\: h\\[/tex]

[tex]\implies \sf \dfrac{1.54 \times 7}{10.78} =\: h\\[/tex]

[tex]\implies \sf \dfrac{\cancel{10.78}}{\cancel{10.78}} =\: h[/tex]

[tex]\implies \sf \dfrac{1}{1} =\: h\\[/tex]

[tex]\implies \sf 1 =\: h[/tex]

[tex]\implies \sf\bold{h =\: 1\: m}\\[/tex]

[tex]\sf\bold{\underline{\therefore\: The\: height\: of\: the\: cylinder\: is\: 1\: m\: .}}\\[/tex]