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Mathematics

The diameters of two circles are 32 cm and 24 cm. Find the radius of the circle having its area equal to sum of the areas of the two given circles.

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Answer

For the first circle,

d1 = 32 cm

r1 = d12\dfrac{d_1}{2} = 322\dfrac{32}{2} = 16 cm

Area1 = π x 162 = 256π cm2

For the second circle,

d2 = 24 cm

r2 = d22\dfrac{d_2}{2} = 242\dfrac{24}{2} = 12 cm

Area2 = π x 122 = 144π cm2

Total area = Area1 + Area2

= 256π + 144π

= 400π cm

Let the radius of the new circle be R.

Area of the new circle = πR2

400π = πR2

400 = R2

R = 400\sqrt{400}

R = 20 cm

Hence, the radius of the new circle is 20 cm.

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