The radius of a large pizza is two times plus 3 inches larger than a small pizza. The area of the small pizza is 33 square inches less than the large pizza. What is the radius of the larger pizza?
Call the small pizza radius r and the large pizza radius R.
R = 2r +3
pi R^2 = pi r^2 -33
= pi*(4r^2 + 6r + 9)
3r^2 + 6r + (33/pi) +9 = 0
Solve that quadratic for r.
Are you sure the problem did not say
"The area of the small pizza is 33 pi square inches less than the large pizza. " ?
The answer would be easier to write down in that case, because the pi factors would cancel out
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To find the radius of the larger pizza, we need to set up equations based on the given information.
Let's say the radius of the small pizza is "r" inches. According to the problem, the radius of the large pizza is two times plus 3 inches larger than the small pizza. Therefore, the radius of the large pizza can be represented as "2r + 3".
The area of a pizza is calculated using the formula A = πr^2, where A is the area and r is the radius.
According to the problem, the area of the small pizza is 33 square inches less than the large pizza. We can set up an equation for this:
A_large - A_small = 33
Substituting the area formulas, we get:
π(2r + 3)^2 - πr^2 = 33
Now, we can solve this equation to find the value of "r".
π(2r + 3)^2 - πr^2 = 33
π(4r^2 + 12r + 9) - πr^2 = 33
4πr^2 + 12πr + 9π - πr^2 = 33
3πr^2 + 12πr + 9π = 33
3πr^2 + 12πr + 9π - 33 = 0
3πr^2 + 12πr + 9π - 33 = 0
This is a quadratic equation in terms of "r". We can solve it by factoring or using the quadratic formula:
r = (-b ± √(b^2 - 4ac)) / (2a)
After substituting the values, we can calculate the value of "r".