Find the percent increase in the area of a circular pizza if the radius is increased from nine inches to ten inches.
area of 9" pizza = 81π
area of 10" pizza = 100π
increase = 19π
percentage increase = 19π/(100π)(100%) = 19%
A=r^2*pi
(10^2*pi)/(9^2*pi)=100/81=1.23456790123
1.23456790123*100%=123.456790123%
123.456790123%-100%=23.456790123%
increse=23.456790123%
A = pi * r^2
A = 3.14 * 81
A = 254.34 sq. inches
Find the area of the larger pizza.
Divide the difference by the area of the smaller pizza.
I should have taken 19π/(81π) for a 23.5% increase
as 'anonymous" and Ms Sue did
sorry about that.
Time to get a strong coffee.
To find the percent increase in the area of a circular pizza, we need to compare the areas before and after the increase in radius. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
First, let's calculate the area of the pizza before the increase in radius. Given that the initial radius is 9 inches, we can use the formula A = π(9)^2 to find the area.
A1 = π(9)^2
Next, we calculate the area of the pizza after the increase in radius. With the new radius being 10 inches, we can substitute this value into the formula.
A2 = π(10)^2
Now, we can find the percent increase by using the following formula:
Percent Increase = ((A2 - A1) / A1) * 100
Substituting the values we calculated earlier:
Percent Increase = ((π(10)^2 - π(9)^2) / π(9)^2) * 100
Simplifying, we get:
Percent Increase = ((π100 - π81)/π81) * 100
Percent Increase = ((100π - 81π) / 81π) * 100
Percent Increase = (19π / 81π) * 100
Simplifying π/π to 1, we get:
Percent Increase = (19/81) * 100
Percent Increase ≈ 23.46%
Therefore, the percent increase in the area of the circular pizza when the radius is increased from nine inches to ten inches is approximately 23.46%.