Final answer:
The volume of a spherical piñata made from 3,000 square inches of material is approximately 15,455 cubic inches, after calculating the radius from the surface area and then using it to find the volume. Therefore, the correct option is B.
Step-by-step explanation:
To find the volume of a spherical piñata using the given material area, we need to use the formulas for the surface area and volume of a sphere. The surface area A of a sphere is given by A = 4πr², where r is the radius. From the problem, we know A = 3,000 square inches.
We first solve for r:
- 3,000 = 4πr²
- r² = ⅓² (3,000) / ⅓² (4π)
- r² = 750 / π
- r = √(750 / π)
Using 3.14 for π:
- r = √(750 / 3.14)
- r ≈ 15.48 inches
Now, we calculate the volume V of the sphere using V = ⅓πr³:
- V = (4/3) × 3.14 × (15.48)³
- V ≈ (4/3) × 3.14 × 3,720.36
- V ≈ 15,454.92 cubic inches
Therefore, the correct option is B.
"Your question is incomplete, probably the complete question/missing part is:"
A company wants to sell spherical piñatas and will use 3,000 square inches of material for each one. What will be the volume of each piñata in cubic inches? (Use 3.14 for π. Round to the nearest integer at the end of your work.)
A) 1000
B) 15,455
C) 15.451
D) 123,609