Question

a sonographer is trying to determine the size of a gallstone. if the stone is spherical and has a diameter of 12 millimeters, what is its volume? a) 452 cubic millimeters b) 904.32 cubic millimeters c) 1.2 cubic centimeters d) 9.0 cubic centimeters

Explanation:

Step1: Find the radius of the sphere

The diameter \( d = 12 \) millimeters, so the radius \( r=\frac{d}{2}=\frac{12}{2} = 6 \) millimeters.

Step2: Use the volume formula for a sphere

The volume formula for a sphere is \( V=\frac{4}{3}\pi r^{3} \). Substitute \( r = 6 \) into the formula:
\( V=\frac{4}{3}\pi(6)^{3}=\frac{4}{3}\pi\times216 = 288\pi \)

Step3: Calculate the numerical value

Using \( \pi\approx3.1416 \), we get \( V = 288\times3.1416=904.778684 \approx 904.32 \) cubic millimeters (the slight difference may be due to different approximations of \( \pi \) used).

Answer:

B) 904.32 cubic millimeters