Two circular pizzas have radii in the ratio 2:3. If the smaller pizza has an area of 100π cm², what is the area of the larger pizza?

Correct — B. Area grows with the square of the radius, so square the ratio before scaling.

Radius ratio: 2 : 3
Area ratio: 2² : 3² = 4 : 9

Larger area = 100π × 9⁄4
= 25π × 9 = 225π cm² → option (b)

Why the others are wrong

• (a)
  265π cm² — 265π ÷ 100π = 2.65, but squaring the radius ratio gives (3⁄2)² = 2.25. The larger area is 2.25 × 100π = 225π, so 265π overshoots by 40π.
• (c)
  215π cm² — 215π ÷ 100π = 2.15, short of the required (3⁄2)² = 2.25. Scaling 100π by 9⁄4 gives exactly 225π, so 215π falls 10π short.
• (d)
  250π cm² — 250π ÷ 100π = 2.5, above the required (3⁄2)² = 2.25. The larger pizza is 2.25 times the smaller, 225π, so 250π overshoots by 25π.

Area scales with the square of any length ratio. Area = πr², so for radii in the ratio a : b the π cancels and the areas are in the ratio a² : b².

Diameters and circumferences are in the same ratio as the radii, so a 2 : 3 ratio of either also gives areas in the ratio 4 : 9.

Key facts

• Area of a circle = πr².
• If two radii are in the ratio a : b, the areas are in the ratio a² : b².
• Circumference = 2πr, so circumferences are in the same ratio as the radii.

Common traps

• Scaling the area by the radius ratio itself: 100π × 3⁄2 = 150π. That skips the square, and 150π is not among the options.
• Multiplying by 4⁄9 instead of 9⁄4, which makes the larger pizza smaller than 100π.

No directly related past PYQ was found.