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
2 answers:
Answer:
Step-by-step explanation:
<u>For old circular garden: </u>
take the radius as r.
then use the formula to find area of circle: πr² ......this is old garden area.
<u>For new enlarged garden: </u>
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:
Step-by-step explanation:
<u>Original diameter is d and new diameter is D and:</u>
<u>Area of original circle:</u>
<u>Area of enlarged circle:</u>
A₂ = πD²/4 = π(2d)²/4 = πd² <u>The ratio of areas:</u>
A₁ / A₂ = πd²/4 ÷ πd² = 1/4 ÷ 1 = 1/4
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Step-by-step explanation