Final answer:
Allison can pour approximately 58 servings of soup from her cylindrical jar into hemispheric bowls with a radius of 6 cm.
Step-by-step explanation:
To determine how many servings of soup Allison can pour into hemispheric bowls from her cylindrical jar, we need to calculate the volumes of both the jar and the bowls, and then divide the volume of the jar by the volume of one bowl.
Volume of the Cylindrical Jar
The formula to calculate the volume of a cylinder is V = πr²h, where V represents volume, r is the radius, and h is the height. For Allison's jar, we have:
- Radius of the jar, r = 14 cm
- Height of the jar, h = 32 cm
Therefore, the volume of the jar is:
V = π(14 cm)²(32 cm) = π(196 cm²)(32 cm) = π(6272 cm³) ≈ 19699.1 cm³
Volume of a Hemispheric Bowl
The volume of a hemisphere is half the volume of a sphere, so the formula is V = ½πr³. The radius of the bowl is 6 cm, thus:
V = ½π(6 cm)³ = ½π(216 cm³) = ½π(108 cm³) ≈ 339.3 cm³
Now to find the number of servings, we divide the volume of the jar by the volume of one bowl:
Number of servings = 19699.1 cm³ / 339.3 cm³ ≈ 58 servings
Thus, Allison can pour approximately 58 servings of soup into the hemispheric bowls.