Question #275
In how many times will increase the square of a circle if its diameter is increased by (a) 2 times, (b) 5 times, (c) m times?
Expert's answer
The radius of the circle is a half of its diameter. So if diameter is increased by m times, the radius increased by m times too. The square is expressed by the formula: S = π*R².
(a) Radius of the circle increased by 2 times. It means that m = 2. So the square of the circle increased by m² = 4 times.
(b) Radius of the circle increased by 5 times. It means that m = 5. So the square of the circle increased by m² = 25 times.
(c) Suppose that the radius was equal to R and became equal to m*R (increased by m times).
So the square of the circle was S = π*R² and became S’ = π(m*R)² = m²*(π*R²) = m²*S. We can see that the square of the circle increased by m² times.
(a) Radius of the circle increased by 2 times. It means that m = 2. So the square of the circle increased by m² = 4 times.
(b) Radius of the circle increased by 5 times. It means that m = 5. So the square of the circle increased by m² = 25 times.
(c) Suppose that the radius was equal to R and became equal to m*R (increased by m times).
So the square of the circle was S = π*R² and became S’ = π(m*R)² = m²*(π*R²) = m²*S. We can see that the square of the circle increased by m² times.
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