Question

The volume of a cylindrical container is 125 cubic centimeters. the height of the container is 6 centimeters. Find the radius of the container. Round your answer to the nearest whole number.

Answer 1

★ Understanding the question :

Here we have the volume of the cylindrical container, that is 125 cm³ and the height of the container is 6 cm. We have to find the radius of the container. So, here we will use the formula of volume of cylinder.

Let's do it !!

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$\underbrace{\underline{\sf{Required\:solution\::}}}$

$\:\::\mapsto\:\sf Volume_{(Container)}\:=\:\pi r^2 h$

★ Values we have :

• Volume of container is 125 cm³.
• Height of container is 6 cm.

★ Putting all vaules :

$\:\::\mapsto\:\sf 3.14\:\times\: r^2\:\times\: 6 \:=\: 125$

$\:\::\mapsto\:\sf r^2\:\times\: 18.8 \:=\: 125$

$\:\::\mapsto\:\sf r^2 \:=\:\dfrac{ 125}{18.8}$

$\:\::\mapsto\:\sf r^2 \:=\:{\dfrac{\cancel{ 125}}{\cancel{18.8}}}$

$\:\::\mapsto\:\sf r^2 \:=\: 6.6$

$\:\::\mapsto\:\sf r \:=\: \sqrt{6.6}$

$\:\::\mapsto\:\bold { r \:=\:\red{ 2.56\:cm}}$

This is the required answer.

$\large\underline{\boxed{\tt{ Radius\:of\:container\:\approx\:\rm\purple{3\:cm}}}}$

Answer 2

Answer:

$\bf Given \begin{cases} \bf Volume = \frak{125\: cm^3} \\ \bf Height = \frak{6 \: cm}\end{cases}$

_____________________________

Now

We know that

${ \boxed { \red{ \underline{ \tt{Volume = \pi {r}^{2} h}}}}}$

Let the radius be r

$\sf \: 125 = \dfrac{22}{7} \times {r}^{2} \times 6$

$\sf \: 125 \times 7 = 22 \times {r}^{2} \times 6$

$\sf \: 875 = 132 \times {r}^{2}$

$\sf \dfrac{875}{132} = {r}^{2}$

$\sf \: 6.63 = {r}^{2}$

$\sf \: \sqrt{6.63 } = r$

$\sf \: 2.57 = r$