if 6 oz of dough are needed to make an 8-in. pizza, how much dough will be needed to make a 16-in. pizza of the same thickness? (compare the areas of the pizza tops)
i don't know what to do
nope. i figured it out. you have to use pi to find the areas of both pizzas and then their ratio is 1:4 so 6*4 = 24
the answers 24. i looked at the answers cus i thought it was 12 too
you do not need pi. It cancels.
r1 = 4 inches
r2 = 8 inches
since thickness is the same:
volume2 = volume1 (pi r2^2 /pi r1^2)
volume2 / volume 1 = (8^2/4^2) = 4
so
volume2 = volume1 * 4
mass2 = 6 * 4 = 24
Well, as an expert in dough-namic calculations, I'm here to help you out! To compare the amount of dough needed, we can look at the areas of the pizza tops since they have a direct relationship with the amount of dough required.
The area of a circle is calculated using the formula A = πr², where A is the area and r is the radius. Now, since we have two pizzas with different radii, we can use the ratio of their areas to determine the dough needed.
For the 8-inch pizza, the radius (r₁) is 8/2 = 4 inches. The area (A₁) can be calculated as A₁ = π(4)².
For the 16-inch pizza, the radius (r₂) is 16/2 = 8 inches. The area (A₂) can be calculated as A₂ = π(8)².
To find the ratio of the areas, we can divide A₂ by A₁: A₂/A₁ = (π(8)²)/(π(4)²).
Thankfully, π cancels out in the division, simplifying the equation: A₂/A₁ = (8²)/(4²).
Calculating that gives us A₂/A₁ = 64/16 = 4.
This means that the area of the 16-inch pizza is four times the area of the 8-inch pizza. So if the 8-inch pizza requires 6 oz of dough, we can simply multiply that by 4 to get the amount of dough needed for the 16-inch pizza.
Therefore, 6 oz of dough would be needed to make a 16-inch pizza of the same thickness. It's dough-lightful, isn't it?
To determine how much dough will be needed to make a 16-in. pizza, we can compare the areas of the two pizzas. The area of a circle can be calculated using the formula: A = πr^2, where A is the area and r is the radius of the circle.
First, let's find the radius of the 8-in. pizza. Since the diameter of the pizza is 8 inches, the radius will be half of that, which is 4 inches.
Now, we can calculate the area of the 8-in. pizza. Using the formula, A = πr^2, we substitute the value of the radius:
A (8-in. pizza) = π(4^2) = π(16) = 16π square inches
Next, let's find the radius of the 16-in. pizza. Again, since the diameter is 16 inches, the radius will be half of that, which is 8 inches.
Now, we can calculate the area of the 16-in. pizza:
A (16-in. pizza) = π(8^2) = π(64) = 64π square inches
As we can see, the area of the 16-in. pizza is four times larger than the area of the 8-in. pizza. Since the thickness of the dough remains the same, we can conclude that four times the amount of dough will be needed for the 16-in. pizza.
Therefore, if 6 oz of dough are needed for an 8-in. pizza, then 4 times the amount, which is 24 oz, will be needed for the 16-in. pizza.