A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 percent larger than the original, by what percentage has the area of logo increased?

Question: A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 percent larger than the original, by what percentage has the area of logo increased?

Solution:
Let the original diameter = D
Original radius = D/2

New diameter = 50% larger = D + 0.5D = 1.5D
New radius = 1.5D/2 = 1.5 × original radius

We know,
Area of a circle = πr²
Original area = π (D/2)² = πD²/4

∴ New area = π (1.5D/2)² = π (0.75D)²
= π × 2.25 × D²/4
= 2.25 × original area

∴ Increase in area = New area - Original area
= 2.25A - A
= 1.25A

∴ Percentage increase = (Increase/Original area) × 100%
= 1.25 × 100
= 125%