Question

lara found the volume of a sphere with a diameter of 10.
laras work
$v = \frac{4}{3}\pi(10^{3})$

1. $v = \frac{4}{3}\pi(1000)$
2. $v = \frac{4000}{3}\pi$ units$^{3}$

analyze laras work. is she correct? if not, what was her mistake?
yes, she is correct.
no, her units should be squared for volume.
no, she should have multiplied 4 and 10 first before applying the exponent.
no, she used the diameter instead of the radius measure.

Explanation:

Step1: Recall the formula for the volume of a sphere

The formula for the volume of a sphere is \( V=\frac{4}{3}\pi r^{3}\), where \( r \) is the radius of the sphere.

Step2: Find the radius from the diameter

Given the diameter \( d = 10\), the radius \( r=\frac{d}{2}=\frac{10}{2} = 5\).

Step3: Analyze Lara's work

Lara used \( r = 10\) (the diameter) in the formula \( V=\frac{4}{3}\pi r^{3}\) instead of using the radius \( r = 5\).

Answer:

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