Given a sphere with radius r, the formula 4r2 gives _____.A.the volumeB.the surface areaC.the radiusD.the cross-sectional area

Break Down the Problem

1. Identify the formula provided: $4r^2$.
2. Consider what geometric properties can be calculated with this formula regarding a sphere.

Relevant Concepts

1. Volume of a Sphere: The formula is $V = \frac{4}{3}\pi r^3$.
2. Surface Area of a Sphere: The formula is $A = 4\pi r^2$.
3. Radius: Denoted simply as $r$.
4. Cross-sectional Area: For a sphere, this is the area of a circle with radius $r$, given by $A = \pi r^2$.

Analysis and Detail

• The formula $4r^2$ directly correlates with the surface area of a sphere, as seen from the standard formula $4\pi r^2$. While the constant $\pi$ is omitted in this expression, the structure matches that of the surface area formula.

Verify and Summarize

• Since $4r^2$ does not match with the volume, radius, or cross-sectional area based on their respective formulas, it aligns with the components of a sphere's surface area.

Final Answer

B. the surface area.