Question

The diameter of a circular chip is doubled to use in a new board game. The area of the new chip will be

Answer 1

Answer: $A_2=\frac{\pi(2D)^{2}}{4}$

Step-by-step explanation:

1. You have the following formula for calculate the area of the original circular chip:

$A_1=\frac{\pi(D)^{2}}{4}$

Where D is the diameter of the circle.

2. Then, if the diameter of the original circular chip is doubled (2D) to use in a new board game, the area of the new chip can be calculated with the following formula:

$A_2=\frac{\pi(2D)^{2}}{4}$

Answer 2

Answer:

The area of the new chip will be 4 times the area of old chip

Step-by-step explanation:

Formula

Area of circle = πr²  where r is the radius if circle

Let d  be the diameter of old circular chip

radius r = d/2

To find the area of old chip

Area = πr² = π(d/2)²

Area = πd²/4

To find the area of new chip

Here diameter = 2d

radius  r = 2d/2 = d

Area = πr² = πd²

Therefore the area of the new chip will be 4 times the area of old chip