Question

noah is working on a geometry problem that involves finding the volume of a sphere with a diameter of 9 units. his work is shown below.
$v = \frac{4}{3}\pi r^3$
$v = \frac{4}{3}\pi(9)^3$
$v = \frac{4}{3}\pi(729)$
$v = 972\pi$ cubic units
is noah’s work correct? explain.
\bigcirc yes, noah’s calculations are correct.
\bigcirc no, noah did not simplify correctly.
\bigcirc no, noah used the diameter instead of the radius in the calculations.
\bigcirc no, noah did not use the correct formula for volume of a sphere.

Explanation:

Step1: Find sphere radius

The diameter is 9 units, so radius $r=\frac{9}{2}=4.5$ units.

Step2: Check Noah's input

Noah substituted $r=9$ (the diameter) instead of the radius into the volume formula $V=\frac{4}{3}\pi r^3$.

Step3: Evaluate error

His core mistake is using diameter in place of radius, leading to an incorrect volume value.

Answer:

No, Noah used the diameter instead of the radius in the calculations.