Question

A circle has a circumference of 48 centimeters. If the radius of the

circle is multiplied by 9, what is the circumference of the new circle?

Answer 1

432 cm

Explanation:

the circumference (C) of a circle is calculated as

C = 2πr ( r is the radius )

If the radius is multiplied by 9 then the circumference will also be increased by a factor of 9

given C = 48 cm

then circumference of new circle = 9 × 48 cm = 432 cm

Answer 2

`\text{According to the condition, circumference,}\\\\~~~~~~~C_1=2\pi r=48~~~~~~~~~~~~~~~~...(i)\\\\\\~~~~~~~C_2 =2\pi \cdot(9r) =18\pi r~~~~~~...(ii)\\\\(ii) / (i)\\\\~~~~~~(C_2)/(C_1) = (18\pi r)/(2\pi r) \\\\\\\implies (C_2)/(48)= 9\\\\\\\implies C_2 = 48* 9\\\\\\\implies C_2 = 432~ \text{cm}\\\\\text{Hence, the new circumference is 432 cm.}`