Volume of ball radius 4 cm Step by Step

Step by step

Question: find the volume of a sphere (a ball) with radius 4 cm.

Put the ball in a cylinder just as wide and just as high.

The ball fills exactly two thirds of that cylinder.

Worked out, that gives the rule for a ball.

The rule has r³: r times r times r.

Careful: it is not 3 times r.

π is a special number for circles.

It is about 3.14.

So the volume is V = 4/3 × π × r³.

V = 43 × π × r³

Now put the numbers in: r = 4.

V = 43 × π × 4³

4³ means 4 times 4 times 4.

That is 64.

4³ = 4 × 4 × 4 = 64

So V = 4/3 × π × 64.

V = 43 × π × 64

None of the numbers divides by 3.

So we multiply and keep the 3 at the bottom: 4 times 64 is 256.

So V = 256π over 3.

We keep π in the answer.

That is the exact answer.

V = 256π3 cm³

To see about how much, put 3.14 for π.

V ≈ 256 × 3.143

256 times 3.14 is 803.84.

V ≈ 803.843

803.84 divided by 3 is about 267.95.

So the volume is about 267.95 cm³.

V ≈ 267.95 cm³

Let's look back.

First: use the rule.

Last: about how much.

Answer

V ≈ 267.95 cm³