Question

Question #de4c6

Answer 1

72 meters

Explanation:

Now I'm sure there's an easy trick but I will solve this algebraically to hopefully show how to really do it.

The formula for area of a circle is `pir^2`. Now, let's say circle A has a radius `a`, and circle B has a radius `b`. The area for circle A would be `pia^2` and the area for circle B would be `pib^2`.

Now if the area of circle B is 36 times greater than the area of circle A, we can translate that into math by saying `area_B = 36*area_A`

Now we'll plug in what we know for `area_B` and `area_A`.
`pib^2=36pia^2`
`pib^2=36pi12^2` (sub in variables)
`b^2=36*12^2` (divide `pi` from both sides)
`b^2=36*144` (solve `12^2`)
`b^2=5184` (simplify right hand side)
`b=72` (take square root of both sides)

Answer 2

`72m`.

Explanation:

Let `r_A and [A]` denote the radius and the area of the circle `A`.

Similarly for circle `B`, we have notations `r_B and [B}`

Given that `[B]=36[A] rArr cancelpir_B^2=36cancelpir_A^2`

`:.r_B^2=36*12^2=(6*12)^2`

`:. r_B=72m`.

Answer 3

`72m` by using the area of similar figures.

Explanation:

All circles are SIMILAR figures.

The corresponding sides of similar figures are in the same ratio.

The AREAS of similar figures are in the same ratio as the
SQUARE of the sides (or any length, in this case the radii).

In this case, we have the smaller radius (r) = 12.
We need the larger Radius (R).

The ratio of the radii is `" "12 : R`

We know that the larger area is 36 times bigger,

So. the ratio of the areas is `1 : 36`

Therefore using the ratio's of the radii SQUARED and the areas:

`12^2/R^2 = 1/36`

`R^2 = (12^2 xx 36)/1 = 5184`

`R = sqrt1584 = 72`