Question

A severe weather siren in a local city can be heard within a radius of 1.3 miles. If the mayor of the city wants a new siren that can cover double the area of the old siren, what should the radius of the new siren be?
(Round to the nearest tenth of a mile.)
a. 3.2 miles
b. 2.4 miles
c. 2.6 miles
d. 1.8 miles

Answer 1

Ok first of all, we find the area that ther 1.5 mile Siren covers using area of a circle,
Radius of a circle = 1.3
Area of a circle = pi * r^2
So area = 1.3 * pi = 4.0840

So since the mayor now wants it double that Area
it means we multiply the area by 2
So 4.808407 * 2 = 9.6168

However the radius the siren covers has changed, so we are to find the new radius
making r subject of formula from area of a circle
Area of a circle = 9.618
Area of a circle = pi*r^2
r = \[sqrt{(Area of a circle)/pi} \]
r = 1.7495

To the nearest 10th, radius becomes 1.8

Answer 2

well the new radius will give 1.753.... not 1.7495, so if you round up you get 1.8