Ms.Jackson decided to do a little shopping after school. She stopped at target to buy two new cake pans. One had a 4in diameter and the other had a 8in diameter. How much greater is the area of the larger pan?
greater by a factor of 4, in the amount of 48π
A = pi * r^2
A = 3.14 * 4
A = 12.56 square inches
Do the same for the 8-inch diameter pan.
To find the area of the cake pans, you need to use the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius.
For the first cake pan with a diameter of 4 inches, the radius (r) would be half of the diameter, so r = 4/2 = 2 inches.
To find the area of this pan, you need to plug the value of the radius into the formula:
A1 = π(2^2) = 4π square inches.
For the second cake pan with a diameter of 8 inches, the radius (r) would be half of the diameter, so r = 8/2 = 4 inches.
To find the area of this pan, you also need to plug the value of the radius into the formula:
A2 = π(4^2) = 16π square inches.
To compare the areas of the two pans, you subtract the smaller area from the larger one:
Area difference = A2 - A1 = 16π - 4π
Since π (pi) is a constant approximately equal to 3.14, you can calculate the difference:
Area difference ≈ (16 - 4) × 3.14
Area difference ≈ 12 × 3.14
Area difference ≈ 37.68 square inches.
Therefore, the area of the larger pan is approximately 37.68 square inches greater than the smaller pan.