A circular pizza has a radius of x cm.
a.write an expression for the area of the pizza?
b write an expression for the area of a pizza with radius that is 5 cm greater
c. How much greater is the second area? write the difference as a simplified expression?
a = πr^2
now just substitute in x or (x+5)
a. The expression for the area of the pizza with radius x cm is A = πx^2.
b. The expression for the area of a pizza with a radius that is 5 cm greater would be A = π(x + 5)^2.
c. To find the difference in the two areas, we need to subtract the first area from the second area.
Difference = Area with greater radius - Area with original radius
Difference = A - A_original
Difference = π(x + 5)^2 - πx^2
To simplify this expression, we can expand and simplify:
Difference = π(x^2 + 10x + 25) - πx^2
Difference = πx^2 + 10πx + 25π - πx^2
The x^2 terms cancel out, and we're left with:
Difference = 10πx + 25π
So the difference between the two areas is 10πx + 25π.
a. The expression for the area of a circular pizza is given by: A = πr^2, where "r" represents the radius of the pizza.
So, for a pizza with a radius of x cm, the expression for the area of the pizza would be A = πx^2.
b. To find the expression for the area of a pizza with a radius that is 5 cm greater, we need to add 5 cm to the original radius (x):
New radius = x + 5 cm
Therefore, the expression for the area of this pizza would be A = π(x+5)^2.
c. To find how much greater the second area is, we need to subtract the area of the first pizza (A = πx^2) from the area of the second pizza (A = π(x+5)^2):
Difference = Area of the second pizza - Area of the first pizza
= (π(x+5)^2) - (πx^2)
= π[(x+5)^2 - x^2]
= π[(x^2 + 10x + 25) - x^2]
= π[10x + 25] (simplified expression for the difference)