I need help on a math question.
Carly makes a rectangular pepperoni pizza using a 12-inch by 16-inch rectangular pan. If Kyle wants to make a circular pepperoni pizza that is approximately the same thickness as Carly’s pizza using the same amount of dough, what should be the diameter of Kyle’s circular pan? Please round your answer to the nearest tenth of an inch.
Thanks for helping!
For this question, you need to find the area of the rectangular pan of pizza first. As you know, you find the area of a rectangle by multiplying the two sides by one another. In this case, that is 12*16 = 192.
Then you have to figure the area of a circle. The equation for that is area = pi*r^2 where r is the radius of the circle.
So we know the area and we know pi so our equation is
192 = 3.14(r^2).
We divide both sides by 3.14 and we get
61.14 = r^2
Take the square root of 61.14, which is 7.8.
So the circular pan needs to be 7.8 inches in radius or 15.6 inches in diameter.
Here the volume of material of the dough is same and the thickness of the pizza is same but only the shape and area are different.The first one is rectangular and the second one is flat cylinderical.
Let the thicknes of the pizza be h inch
The volume of the rectangular shape = length*breadth*h =16*12*h...........(1)
The volume of the circular pizza = pi*radius^2*thickness=pi*(diamete/2)^2*thicknes.
Since the volume represented at (1) and (2) are same,
(pi*d^2/4)h = 16*12*h) The h gets cancelled. So solving for, d,
d = sqrt(16*12*4/pi) = 15.63528 inch =15.6 inch
When the thickness of the pizza as well as the amount of dough used for the rectangular and the circular pizzas are same, the areas of the pizza will also be same.
The area of rectangular pizza of 12" x 16" is given by the formula:
Area of rectangle = A = Width x Length = 12 x 16 = 192 sq.inch
The area of a circle is given by:
Area of circle = A = (pi/4) x d^2
Where: d = diameter of circle
Therefore diameter of circular pizza with area = A is given by:
d = [A/(pi/4)]^1/2 = 2 x (A/pi)^1/2
Value of A = 192 and pi is a constant with value 3.141
d = = 2 x (192/3.141)^1/2 = 2 x 7.818 = 15.636 = 15.6"
Diameter of circular pan = 15.6"