Question

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 ?

Answer 1

EF

Explanation:

Answer 2

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.