Answer:
The radius of the scoop is r = 3.1 cm
Step-by-step explanation:
Since 3 gallons yields 90 scoops, and 1 gallon = 3785 cm³.
3 gallons = 3 × 3785 cm³ = 11355 cm³
So we have 11355 cm³ in 3 gallons which is also the volume of 90 scoops.
Since 90 scoops = 11355 cm³, then
1 scoop = 11355 cm³/90 = 126.2 cm³
Now, if each scoop is a sphere, the volume is given by V = 4πr³/3 where r is the radius of the scoop. Since we need to find the radius of the scoop, r, making r subject of the formula, we have
r = ∛(3V/4π)
Substituting V = 126.2 cm³, we have
r = ∛(3× 126.2 cm³/4π)
= ∛(378.6 cm³/12.57)
= ∛30.13 cm³
= 3.1 cm
So, the radius of the scoop is r = 3.1 cm
