Question

geometry—session 2: calculator
part b
daniel wants to reshape the other chunk of clay to make a set of clay spheres. he wants each sphere to have a diameter of 4 inches. find the maximum number of spheres that daniel can make from the chunk of clay. show your work.
enter your answer and your work in the box provided.

Explanation:

Step1: Recall Sphere Volume Formula

The volume \( V \) of a sphere is given by \( V = \frac{4}{3}\pi r^3 \), where \( r \) is the radius. The diameter is 4 inches, so the radius \( r=\frac{4}{2}=2 \) inches.

Step2: Calculate Volume of One Sphere

Substitute \( r = 2 \) into the formula: \( V=\frac{4}{3}\pi(2)^3=\frac{4}{3}\pi\times8=\frac{32}{3}\pi\approx\frac{32}{3}\times3.14\approx33.51 \) cubic inches.

Step3: Assume Clay Volume (Missing in Image, Assume From Part A, e.g., If Clay Volume is 100.53)

Suppose the volume of the clay chunk (from Part A, common problem setup) is \( 100.53 \) cubic inches (e.g., if it was a cylinder with \( r = 3 \), \( h = 4 \), \( V=\pi r^2h=\pi\times9\times4 = 36\pi\approx113.1 \), but let's use a common example where clay volume is \( 100.53 \)). Then divide total clay volume by one sphere's volume: \( \frac{100.53}{33.51}\approx3 \). (Note: Actual volume depends on Part A, but process is as above.)

Answer:

(Depends on clay volume; for example, if clay volume is \( 100.53 \) in³, answer is 3. Show work with sphere volume formula and division.)