Question

The diameter of two circles are in the ratio of 4 : 3 and sum of the their areas is equal to the area of the circle, whose radius is 5cm .Find the diameter of the two circles.
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Answer 1

Answer:Define x:

Diameter =  4 : 3

Let x be the constant ratio

Diameter =  4x : 3x

Find the radius in term of x:

Radius = Diameter ÷ 2

Radius =  (4x ÷ 2)  : (3x ÷ 2)

Radius =  2x  : 1.5x

Find the first area:

Area = πr²

Area = π(2x)²

Area = 4πx²

Find the second area:

Area = πr²

Area = π(1.5x)²

Area = 2.25πx²

Find the area of the circle with radius = 5 cm:

Area = πr²

Area = π(5)²

Area = 25π

Solve x:

4πx² + 2.25πx² = 25π

6.25πx² = 25π

x² = 4

x = 2

Find the diameter:

First circle's diameter = 4x = 4(2) = 8 cm

Second circle's diameter = 3x = 3(2) = 6 cm

Answer: The diameters are 8 cm and 6 cm

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Step-by-step explanation:

Answer 2

Step-by-step explanation:

Define x:

Diameter = 4 : 3

Let x be the constant ratio

Diameter = 4x : 3x

Find the radius in term of x:

Radius = Diameter ÷ 2

Radius = (4x ÷ 2) : (3x ÷ 2)

Radius = 2x : 1.5x

Find the first area:

Area = πr²

Area = π(2x)²

Area = 4πx²

Find the second area:

Area = πr²

Area = π(1.5x)²

Area = 2.25πx²

Find the area of the circle with radius = 5 cm:

Area = πr²

Area = π(5)²

Area = 25π

Solve x:

4πx² + 2.25πx² = 25π

6.25πx² = 25π

x² = 4

x = 2

Find the diameter:

First circle's diameter = 4x = 4(2) = 8 cm

Second circle's diameter = 3x = 3(2) = 6 cm

Answer: The diameters are 8 cm and 6 cm

hope it is helpfull