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

Let's analyze Lara's work step by step to verify her calculations regarding the volume of a sphere.

The formula for the volume \( V \) of a sphere is given by:

\[
V = \frac{4}{3} \pi r^3
\]

Where \( r \) is the radius of the sphere. The radius \( r \) is half of the diameter. Since the diameter given is 10, the radius is:

\[
r = \frac{10}{2} = 5
\]

Now, substituting the radius into the volume formula:

\[
V = \frac{4}{3} \pi (5^3)
\]

Calculating \( 5^3 \):

\[
5^3 = 125
\]

Now substituting back into the volume formula:

\[
V = \frac{4}{3} \pi (125) = \frac{500}{3} \pi
\]

So, the correct volume is:

\[
V = \frac{500}{3} \pi \text{ cubic units}
\]

Now let's analyze Lara's work:

1. Lara used the diameter instead of the radius measure. Instead of using the radius (5), she used the diameter (10) directly in her calculations, which is incorrect.

**Conclusion:** The correct answer is: **No, she used the diameter instead of the radius measure.**