Answered

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15. Three concentric circles whose radii are in the ratio 2:3:5. If the area of the smallest circle is
36pi, what would be the area of the largest circle?​

Sagot :

Rktmobilezidn

Area of Circle is given by the formula:

A = πr²

where

A = Area

π = 3.14

r = radius

Let's solve for radius (r) of smallest circle as the area is given as 36π.

solve for radius of smallest circle,

A = πr²

36π = π r²

r² = 36π / π

r² = 36

r = √36

r = 6

so, radius of smallest circle = 6

now we use the given ratios to solve for the radius of the largest circle,

2 : 3 : 5 = 6 : radius of mid circle : radius of largest circle

let's use the ratio where there is only 1 unknown,

2 : 5 = 6 : radius of largest circle

2 (radius of largest circle) = (6)(5)

radius of largest circle = 30/2

radius of largest circle = 15

so now we have radius of largest circle = 15

It's time to find Area of largest circle,

A = πr²

A = π (15)²

A = 225π units²

so the Area of Largest Circle is 225π

or you can express  it as:

A = 225π

A = 225 (3.14)

A = 706.5 units²

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