Answer: Circle.
- A Square
- B Equilateral triangle
- C Circle
- D Regular hexagon
Correct answer: C. Circle
Explanation: Isoperimetric inequality: 4πA ≤ P², with equality iff the curve is a circle. For circle: P=2πr, A=πr², giving 4π(πr²)=4π²r²=P². No other shape achieves this equality. Ans: Circle.
Three standard 3D solids and their key formulas: a cylinder's volume scales with the full height, a cone's volume is exactly one-third of the cylinder with the same base and height, and a sphere's volume and surface area both follow distinct r-based formulas worth memorising separately.
Concept context
Perimeters, areas, and volumes of 2D and 3D shapes