A can is a cylinder with radius 3 cm and height 8 cm. Using 3.14 for… Step by Step

Step by step

The question

Question: find the volume of a cylinder with radius 3 and height 8.

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Circle times height

The top is a circle.

A circle's area is π × r².

π is a special number for circles: the way round is about 3.14 times the way across.

Like a box: one layer, times the number of layers.

Here the bottom layer is the circle.

Each 1 unit up is one more layer: 8 layers.

So the volume is circle area times height: V = π × r² × h.

V = π × r² × h

Now put the numbers in: r = 3 and h = 8.

V = π × 3² × 8

3² means 3 times 3.

That is 9.

3² = 3 × 3

= 9

So V = π × 9 × 8.

V = π × 9 × 8

9 times 8 is 72.

So V = 72π.

We keep π in the answer.

That is the exact answer.

V = 72π

2 About how much

To see about how much, put 3.14 for π.

V ≈ 72 × 3.14

72 times 3.14 is 226.08.

So the volume is about 226.08 cubic units.

V ≈ 226.08

3 Pick the choice

Our answer is V ≈ 226.08.

That is choice C.

C) 226.08

4 Why not the others

A is 75.36.

Wrong: forgot to square the radius.

A) 75.36 ✗ forgot to square the radius

B is 150.72.

Wrong: 2πrh: that is the side's area.

B) 150.72 ✗ 2πrh: that is the side's area

D is 602.88.

Wrong: squared the height, not the radius.

D) 602.88 ✗ squared the height, not the radius

Let's look back.

First: circle times height.

Then: about how much.

Then: pick the choice.

Last: why not the others.

Answer