Question

Find the diameter of the circle whose area is equal to the sum of the areas of two circles diameters 20cm and 48cm.​

Answer 1

Answer:

area of a circle= πr^2

diameter of the 1st circle=20cm so r=20/2= 10cm

area= 100π

diameter of 2nd circle = 48cm so r= 48/2=24cm

area=576π

area of the big circle= 100π+576π= 676π

r^2=676, r= √676=26 cm

diameter= 26*2=52

Answer 2

Given:-

• The diameter of one circle = d' = 20 cm
• R' = d'/2 = 10 cm
• The diameter of another circle = d" = 48 cm
• R" = d"/2 = 24 cm

Find:-

Diameter of the circle whose area is equal to the sum of area of two circles.

Solution:-

We know that -

$\large\purple {\sf {\pmb{Area \: of \: circle \: = πr²}}}$

According to question,

Sum of areas of two circle is equal to area of circle.

πr² = π(r')² + π(r")²

Substitute the known values in above formula

$⇒ πr² = π(10)² + π(24)²$

$⇒ r² = 100 + 576$

$⇒ r² = 676$

$⇒ r = √676$

$⇒ r = 26 cm$

So, diameter of circle = 2r

$⇒ 2(26)$

$\large\purple {\sf{{⇒ 52 cm}}}$