Question

Lara found the volume of a sphere with a diameter of 10.

V = 4
3
π(103)

1. V = 4
3
π(1000)

2. V = 4000
3
πunits3

Analyze Lara’s work. Is she correct? If not, what was her mistake?
Yes, she is correct.
No, she used the diameter instead of the radius measure.
No, she should have multiplied 4 and 10 first before applying the exponent.
No, her units should be squared for volume.

Answer 1

No, she used the diameter instead of the radius measure.

Explanation:

The formula for the sphere is:

`\pi (4)/(3) r^(3)`

So she should have calculated the radius before inserting the values into the formula, the radius is half the diameter, so the radius of that sphere is 5.

In order to calculate it right you have to put 5 instead of the 10 so teh formula would look like this:

`\pi (4)/(3) r^(3)`

`\pi (4)/(3) 5^(3)`

`\pi (4)/(3)(125)`

`250\pi }`

The answer would be:

`250\pi }`

Answer 2

No, she used the diameter instead of the radius measure.

Explanation:

we know that

The volume of the sphere is equal to

`V=(4)/(3)\pi r^(3)`

we have

`r=10/2=5\ units` ----> the radius is half the diameter

substitute

`V=(4)/(3)\pi (5)^(3)`

`V=(500)/(3)\pi\ units^(3)`