A sphere of radius rcm has the same volume as cylinder of radius 3cm and height 4cm. Find the value of r

Analyze the question: A sphere and a cylinder have equal volumes. We know the cylinder's radius (3 cm) and height (4 cm), and we need the sphere's radius r.

Concept:

• Volume of a sphere = (4/3)πr³
• Volume of a cylinder = πR²h

Solution:

Cylinder volume = π(3)²(4) = 36π cm³

Set the volumes equal:

(4/3)πr³ = 36π

Divide both sides by π:

(4/3)r³ = 36

Multiply both sides by 3/4:

r³ = 36 × 3/4 = 27

r = ∛27 = 3

Check: Sphere volume = (4/3)π(27) = 36π, which matches the cylinder's volume.

Answer: r = 3 cm, which is option C.

Tip: In "equal volume" questions, cancel π from both sides right away. This leaves simple numbers, and you can often recognise perfect cubes like 8, 27, 64 and 125 quickly.