Question

the volume of a cylinder is 6600cmcube.what will be its height it its circular base has a radius of 10cm​

Answer 1

Given -

• Volume of cylinder = 6600cm³

• Base radius of cylinder = 10 cm

To find -

• Height of the Cylinder

Formula used -

• Volume of cylinder = πr²h

Solution -

In the question, we are provided with the volume and the base radius of a cylinder, and we need tk find it's height, for that we will use the formula of volume of cylinder, and will put the given values, and then we will do the further the question. Let's do it!

According to question -

Base radius = 10 cm

Volume = 6600 cm³

Height = h

Volume of cylinder = πr²h

Where -

π = $\sf\dfrac{22}{7}$

r = Radius

h = Height

On substituting the values -

$\sf \longrightarrow \: volume \: = \pi \: {r}^{2}h \\ \\ \\ \sf \longrightarrow \: 6600 {cm}^{3} \: = \dfrac{22}{7} \times {(10 \: cm)}^{2} \times h \\ \\ \\ \sf \longrightarrow \: 6600 {cm}^{3} \: = \dfrac{22}{7} \: \times \: 100 \: cm \: \times \: h \\ \\ \\ \sf \longrightarrow 6600 {cm}^{3} \: = \dfrac{2200}{7} \: \times \: h \\ \\ \\ \sf \longrightarrow \: 6600{cm}^{3} = \: 314.28 \: \times \: h \\ \\ \\ \sf \longrightarrow \: h \: = \dfrac{6600}{314.28} \\ \\ \\ \sf \longrightarrow \: h \: = 21cm \: \: (approx)$

$\therefore$ The height of the given Cylinder is 21cm (approx)

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Answer 2

Given :

• The Volume of cylinder = 6600 cm³
• The Base radius of cylinder = 10 cm

To Find :

• The Height of the Cylinder

Solution :

We have,

• $\bf Volume \: of \: cylinder = 6600 \: cm^3$
• $\bf Base \: radius \: of \: cylinder = 10 \: cm$

We know that,

$\boxed{\bf Volume \: of \: cylinder = \pi r^2h}$

Where,

• $\bf \pi = \dfrac{22}{7}$
• $\bf r = Radius$
• $\bf h = Height$

Substituting the given values we get,

$:\implies\bf 6600 = \dfrac{22}{7} \times 10^2 \times h$

$:\implies\bf 6600 = \dfrac{22}{7} \times 100 \times h$

$:\implies\bf 6600 = \dfrac{2200 h}{7}$

$:\implies\bf 2200 h = 46200$

$:\implies\bf h = \cancel{\dfrac{46200}{2200}}$

$:\implies\bf h = 21 \: (approx)$

∴ The height of the given Cylinder is 21 cm (approx)

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$\qquad\boxed{\underline{\underline{\purple{\bigstar \: \bf\:Additional\:Information \:\bigstar}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Surface \: area \: of \: cylinder \: = \: 2 \pi rh + 2 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Lateral \: area \: of \: cylinder \: = \: 2 \pi rh}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Base \: area \: of \: cylinder \: = \: \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Height \: of \: cylinder \: = \: \dfrac{v}{\pi r^{2}}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Radius \: of \: cylinder \: = \:\sqrt \dfrac{v}{\pi h}}}}$

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