Question

If the radius of a circle is tripled, by how many times does It's circumference increase? How many times does it's area increase?

Answer 1

A)The circumference of a cirlce with radius r is

S=2⋅π⋅r

hence if the radius is tripled hence the new radius is r'=3⋅r

then the new circumference is S'

S'=2⋅π⋅r'=2⋅π⋅(3⋅r)=3⋅(2⋅π⋅r)=3⋅S

Finally the circumference will be tripled.


B)

Let the radius of the circle is = r

Then the area of the circle = π r²

Now double radius = 2 r

Then the new area = π (2 r)²

= π × 4 × r²

= 4 (π r²)

If the radius of the sphere is double then the area will become four times.