Question

Find the volume of the cylinder.

Answer 1

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,

`\small\boxed{ \rm{ Radius = (diameter)/(2)}}`

Substituting the values we get

`\small\sf{ Radius = (4)/(2) = 2 \: cm}`

Now we will calculate the volume

`\small \boxed{\sf{ Volume_((cylinder)) = πr²h}}`

Where,

• r stand for radius
• h stand for height

`\small\bf{ Volume_((cylinder)) = 3.14 × 2² × 3 }`

`\small\rm Volume_((cylinder)) = 3.14 × 2 * 2× 3`

`\small\rm{ Volume_((cylinder)) = 37.68 \: cm ³}`

• Hence the volume is 37.68 cm³.

Answer 2

12π ≈ 37.7 cubic centimeters

Explanation:

The volume of the cylinder can be found using the appropriate formula.

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dimensions

The cylinder is marked as having a diameter of 4 cm, and a height of 3 cm. The radius of the cylinder is half the diameter:

r = d/2

r = (4 cm)/2 = 2 cm

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formula for volume

The formula for the volume of a cylinder is ...

V = πr²h . . . . . . where r is the radius and h is the height

Using the dimensions given, we find the volume to be ...

V = π(2 cm)²(3 cm) = π(4 cm²)(3 cm) = 12π cm³

Written as a decimal, the volume is about ...

12π cm³ ≈ 37.70 cm³ . . . . volume of the cylinder

_____

Additional comment

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