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If the diameter of circle a measures half of the diameter of circle b, then the area of circle b is how many times the area of circle a ?

User Fiodor
by
8.4k points

2 Answers

3 votes

Answer:

EF

Explanation:

User Nicholas Siegmundt
by
8.1k points
4 votes
Circle b:

Diameter = x

Radius =
(x)/(2)

Area =
\pi r^(2) = \pi ( (x)/(2) )^(2) = ( \pi x^(2) )/(4)

Circle a:

Diameter =
(x)/(2)

Radius =
(x)/(2) * (1)/(2) = (x)/(4)

Area =
\pi r^(2) = \pi ( (x)/(4) )^(2) = ( \pi x^(2) )/(16)

Thus,

Area of circle b to area of circle a

=
( \pi x^(2) )/(4) ÷
( \pi x^(2) )/(16)

=
( \pi x^(2) )/(4) ×
( 16 )/(\pi x^(2))

= 4

Hence, the area of circle b is 4 times the area of circle a.
User Trilla
by
8.8k points

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