The radius of a sphere is 21cm. If s and v represent the curved surface area and volume respectively, what is s : v? (take π = 3.142)

Analyze the question: We need the ratio of the surface area of a sphere (s) to its volume (v) when r = 21 cm.

Concept:

• Surface area of a sphere: s = 4πr²
• Volume of a sphere: v = (4/3)πr³

Solution:

s : v = 4πr² : (4/3)πr³

Divide both by 4πr²:

s : v = 1 : (r/3)

With r = 21:

r/3 = 21/3 = 7

So s : v = 1 : 7

The value of π cancels out, so you don't need 3.142 at all.

Check with numbers:

• s = 4 × 3.142 × 441 = 5542.2 cm²
• v = (4/3) × 3.142 × 9261 = 38,799 cm³ (approx.)
• 5542.2 : 38,799 = 1 : 7.0 ✓.

Answer: The ratio is 1 : 7, which is option B.

Tip: For a sphere, s : v = 3 : r, which gives 1 : r/3. Just divide the radius by 3. When the radius is a multiple of 3, the ratio simplifies quickly. Also, π usually cancels in ratios, so don't waste time multiplying it out.