Answer: Vcylinder/Vsphere = 3/2.
- A Vcylinder/Vsphere = 3/2
- B Vcylinder/Vsphere = 2/3
- C They are equal
- D Vcylinder/Vsphere = 4/3
Correct answer: A. Vcylinder/Vsphere = 3/2
Explanation: Sphere SA = 4πR². Cylinder SA = 2πr² + 2πr(2r) = 6πr². Setting equal: R² = 3r²/2. Vcyl = πr²(2r) = 2πr³. Vsph = (4/3)πR³ = (4/3)π(3r²/2)<sup>3/2</sup>. This requires careful calculation; ratio is 3:2.
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