If area of a circle C1 is equal to the sum of areas of two circles with radii 4 and 3 cm, then the radius of circle C1 is equal to

5 cm

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6 cm

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7 cm

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8 cm

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Solution

The correct option is A 5 cm
Area of circle C1 = Area of the other two circles
Area of a circle = $π r^{2}$
Area of C1 = $π \times 4^{2}$ + $π \times 3^{2}$
Area of C1 = $π \times 16 + π \times 9$
Area of C1 = $π (16 + 9)$
Area of C1 = = $π \times 25$
Area of C1 = = $π \times 5^{2}$
Hence, the radius of C1 is equal to 5 cm

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If area of a circle C1 is equal to the sum of areas of two circles with radii 4 and 3 cm, then the radius of circle C1 is equal to

The correct option is A 5 cmArea of circle C1 = Area of the other two circles Area of a circle = πr2 Area of C1 = π×42 + π×32 Area of C1 = π×16+π×9 Area of C1 = π(16+9) Area of C1 = = π×25 Area of C1 = = π×52 Hence, the radius of C1 is equal to 5 cm