Question

A circular garden is enlarged so that the new diameter is twice the old diameter. What is the ratio of the original area to the enlarged area? Express your answer as a common fraction.

I do not understand WHY the answer is 1/4 I do not understand why it is k^2 and all that. HELP I am giving LOTS of points

Answer 1

• Explained briefly below.

Explanation:

For old circular garden:

take the radius as r.

then use the formula to find area of circle: πr² ......this is old garden area.

For new enlarged garden:

the radius is twice the old radius so, radius = 2 * r = 2r ......enlarged radius

now find area for this new garden: π(2r)² → 4πr²

In common fractions: (old garden)/(new garden)

: ( πr² ) / ( 4πr² )

: 1/4

Answer 2

• 1/4

Explanation:

Original diameter is d and new diameter is D and:

• D = 2d

Area of original circle:

• A₁ = πd²/4

Area of enlarged circle:

• A₂ = πD²/4 = π(2d)²/4 = πd²

The ratio of areas:

• A₁ / A₂ =
• πd²/4 ÷ πd² =
• 1/4 ÷ 1 =
• 1/4