Question

if the area of a circle whose radius is 5 cm is increased to four times, then find the changed radius

Answer 1

Answer:

10 cm

Step-by-step explanation:

Area of a circle =  pie × (radius)²

Radius = 5 cm

Area of a circle = (22/7) × 5²

A = (22/7) × 25 cm²

Area increased to 4 times so

An = 4 × A

An = 4 × (22/7) × 25 cm²

An = Pie × (new Radius)²

An = (22/7) (Rn)²

(22/7) (Rn)² = 4 × (22/7) × 25

Rn² = 100

Rn = 10 cm

New radius = 10 cm

Answer 2

Area of circle = πr² = 3.14 × 5² = 78.5 cm²

New circle area = 78.5 × 4 = 314 cm²

Now, πr² = 314 cm²

r² = 314 ÷ π = 314 ÷ 3.14 = 100

∴ r =√100 = 10 cm

OR

area of first circle = πr² = 25 π

area of new circle = 25π × 4 = 100π

Area = πr² = 100 π

⇒ r² = 100 π ÷ π = 100

⇒r = √100 = 10 cm