Alex makes a 14 inch diameter pizza, which includes a 1 inch crust. Donald wants to make a 10 inch diameter pizza with the same percent of crust as Alex's pizza. To the nearest tenth of an inch, approximately how wide will the crust be on Donald's pizza?
14^2/15^2 = .871
r^2/10^2 = .871
r = 9.3
so, the crust edge will be 0.7 inch
To find out how wide the crust will be on Donald's pizza, we need to calculate the crust's width as a percentage of the diameter.
Step 1: Calculate the circumference of Alex's pizza
The circumference of a circle is calculated using the formula: C = πd, where C is the circumference and d is the diameter.
Given that the diameter of Alex's pizza is 14 inches, we can calculate the circumference: C = π(14) ≈ 43.98 inches.
Step 2: Calculate the crust width on Alex's pizza
The crust width is given as 1 inch, so we can calculate the percentage of the crust relative to the circumference: crust percentage = crust width / circumference * 100%.
crust percentage = 1 / 43.98 * 100 ≈ 2.27%.
Step 3: Calculate the diameter of Donald's pizza
Since we want to maintain the same crust percentage, we can calculate how wide Donald's crust will be by multiplying the diameter by the percentage: crust width = crust percentage * diameter / 100.
Given that Donald's pizza has a diameter of 10 inches, we can calculate the crust width: crust width = 2.27 * 10 / 100 ≈ 0.227 inches.
To the nearest tenth of an inch, the crust on Donald's pizza will be approximately 0.2 inches wide.
To find out how wide the crust will be on Donald's pizza, we first need to determine the proportion of the crust to the diameter of Alex's pizza.
Alex's pizza has a 14-inch diameter, with a 1-inch crust. So, the diameter of the pizza without the crust is 14 inches - 2 * 1 inch = 14 - 2 = 12 inches.
Now, we can calculate the proportion of the crust on Alex's pizza by dividing the width of the crust (1 inch) by the diameter without the crust (12 inches).
Proportion of crust on Alex's pizza = 1 inch / 12 inches.
To find out how wide the crust will be on Donald's pizza, we need to use the same proportion for his 10-inch diameter pizza.
Crust width on Donald's pizza = Proportion of crust on Alex's pizza * Diameter of Donald's pizza without crust.
Plugging in the values:
Crust width on Donald's pizza = (1 inch / 12 inches) * (10 inches - 2 * crust width on Donald's pizza).
Since we don't know the crust width on Donald's pizza, we'll represent it as 'x':
Crust width on Donald's pizza = (1/12) * (10 - 2x).
To solve this equation, we'll simplify it:
12 * Crust width on Donald's pizza = 10 - 2x.
Now, we can solve for x:
12 * x = 10 - 2x.
12x + 2x = 10.
14x = 10.
x = 10/14.
x ≈ 0.7.
So, to the nearest tenth of an inch, approximately how wide the crust will be on Donald's pizza is 0.7 inches.