Question

what is the diameter of a circle whose area is equal to the sum of the areas of two circles of radii 40 cm and 9cm

Answer 1

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Answer 2

Answer:

Diameter is 82 cm.

Step-by-step explanation:

The area of circle is

$Area=\pi r^2$

The area of a circle is equal to the sum of the areas of two circles of radii 40 cm and 9cm.

Sum of area of two small circles is

$Area=\pi (49)^2+\pi (9)^2$

$Area=\pi [(49)^2+(9)^2]$

$Area=\pi (1681)$

$Area=\pi (41)^2$

Let radius of big circle is R. So, the area of big circle is

$\pi R^2=\pi (41)^2$

R = 41

It means the radius of big circle is 41 cm and diameter is 82 cm.