Find the volume of the cylinder.

You probably noticed that we used the units in the formula along with the numbers. Units abbreviations can be manipulated algebraically the same way any other variable can be:

x · x = x²

cm · cm = cm²

Computing the volume in more steps, we have ...

V = π(2 cm)²(3 cm)

= π(2 cm)(2 cm)(3 cm) . . . . expanding the square term

= π(2)(2)(3)(cm)(cm)(cm) . . . . we can rearrange the factors of a product

= π(12)(cm³)

= 12π cm³

spbankingandsscserie spbankingandsscserie · Answer 2 · 2022-06-10T09:42:45+02:00

Explanation -:

In this question we are provided with the diameter of the cylinder and height of the cylinder. We are asked to calculate the volume of the cylinder. As we know that volume of a cylinder = πr²h units³. In this formula r stand for radius h stand for height but we are provided with the diameter. So, first we will find the radius of the cylinder and then we will find the volume of the cylinder.

Let us solve this problem.

We know,

[tex] \small\boxed{ \rm{ Radius = \dfrac{diameter}{2}}}[/tex]

Substituting the values we get

[tex] \small\sf{ Radius = \dfrac{4}{2} = 2 \: cm}[/tex]

Now we will calculate the volume

[tex] \small \boxed{\sf{ Volume_{(cylinder)} = πr²h}}[/tex]

Where,

r stand for radius
h stand for height

[tex] \small\bf{ Volume_{(cylinder)} = 3.14 × 2² × 3 }[/tex]

[tex] \small\rm Volume_{(cylinder)} = 3.14 × 2 \times 2× 3 [/tex]

[tex] \small\rm{ Volume_{(cylinder)} = 37.68 \: cm ³}[/tex]

Hence the volume is 37.68 cm³.