Question

The area of a circle is directly proportional to the square of its radius. If a circle with a radius of 3 cm has an area of 9 cm³, what will be the area of a circle with a radius of 6 cm?

Answer 1

36 cm^(2)

Explanation:

To solve for the variation,

`a \alpha {r}^(2) \\ a = k {r}^(2)`

Where a is area, r is radius and k is a constant.

Making k the subject,

`k = \frac{a}{ {r}^(2) }`

Here, we would have to find the constant k a= 9 and r = 3

`k = \frac{9 \: {cm}^(2) }{ {(3 \: cm)}^(2) } = 1`

Therefore k = 1.

Now that we have found the constant k,

We can now solve for others

`a = (1) {(6 \: cm)}^(2) = 36 \: {cm}^(2)`