Suppose you have one circle with a radius of 5.0 cm and a second circle with a radius of 3.0 cm. By what factor is the area of the first circle larger than the area of the second circle?

Suppose you have one circle with a radius of 5.0 cm and a second circle with a radius of 3.0 cm. By what factor is the area of the first circle larger than the area of the second circle?

Answer

1. Identify the formula for the area of a circle: The area of a circle is given by A = pi * r^2, where 'r' is the radius. 2. Calculate the area of the first circle (A1): Given a radius of 5.0 cm, A1 = pi * (5.0 cm)^2 = 25.0 * pi cm^2. 3. Calculate the area of the second circle (A2): Given a radius of 3.0 cm, A2 = pi * (3.0 cm)^2 = 9.0 * pi cm^2. 4. Determine the factor by which the first area is larger: Divide the area of the first circle by the area of the second circle. Factor = A1 / A2 = (25.0 * pi) / (9.0 * pi) = 25.0 / 9.0. 5. Final calculation: 25 / 9 is approximately 2.78. Therefore, the area of the first circle is approximately 2.78 times larger than the area of the second circle.