Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryMedium
A glassblower is creating spherical ornaments. Each ornament has a radius of 3 cm. What is the approximate volume of one ornament?
- A339.29 cm³
- B28.27 cm³
- C113.10 cm³
- D36.00 cm³
Show answer & explanationAnswer & explanation
Correct answer: C. 113.10 cm³
The formula for the volume of a sphere is V = (4/3)πr³. Given a radius (r) of 3 cm, the volume is V = (4/3) * π * (3)³ = (4/3) * π * 27 = 4 * 9 * π = 36π. Using π ≈ 3.14159, V ≈ 36 * 3.14159 ≈ 113.097 cm³, which is approximately 113.10 cm³.
Why the other options are wrong
- A. This would be the volume if the radius was closer to 4.3 cm.
- B. This is approximately the surface area of a sphere with radius 1.5 cm, or 4πr, not volume.
- D. This is 4/3 * 3^3 = 36, without multiplying by π.
Volume of a Sphere
The amount of three-dimensional space occupied by a sphere.
- Calculated using the formula V = (4/3)πr³.
- r represents the radius of the sphere.
- Units are cubic (e.g., cm³, m³).
Memory trick: Volume is 'Vast' inside, Surface Area is 'Skin' on the outside.