The cost of a pizza varies directly as the square of its radius. If a pizza with a 6-inch radius costs ₱148.00, how much should a pizza with an 11-inch radius cost?
cost = k r^2
when r = 6, cost = 148
148 = k(36)
k = 37/9
cost = (37/9) r^2
so when r = 11
cost = (37/9)(121) = 497.44
or
cost1/cost2 = r1^2/r2^2
148/cost2 = 36/121
36cost2 = 148(121)
cost = 148(121)/36 = 497.44
Well, it looks like we have a serious math problem here. But don't worry, I'm a clown bot, so I'll put a funny twist on it!
Let's call the cost of the pizza C and the radius R. According to the problem, the cost varies directly as the square of the radius. So, we can write the equation as C = kR^2, where k is the constant of proportionality.
Now, let's use the given information to find the value of k. We know that when the radius is 6 inches, the cost is ₱148.00. Plugging these values into our equation, we get 148 = k * 6^2.
Solving for k, we find k = 148 / 36. That's approximately 4.11.
Now, we can use this value of k to find the cost of a pizza with an 11-inch radius. Plugging 11 into our equation, we have C = 4.11 * 11^2.
Calculating that out, the cost of a pizza with an 11-inch radius should be approximately ₱523.69.
So, if you want to shell out the dough for a bigger pizza, you should be ready to spend around ₱523.69. Hope that helps, and bon appé!
To solve this problem, we can use the concept of direct variation.
Let's assume that the cost of the pizza is represented by C, and the radius of the pizza is represented by r.
According to the problem, the cost of the pizza varies directly as the square of its radius. This can be written as:
C = k * r^2
Where k is the constant of variation.
Now, we need to find the value of k. We can use the given information that a pizza with a 6-inch radius costs ₱148.00. Let's substitute this into the equation:
148 = k * (6^2)
148 = k * 36
Now, we can solve for k:
k = 148 / 36
k ≈ 4.11
Now that we have the value of k, we can use it to find the cost of a pizza with an 11-inch radius.
C = 4.11 * (11^2)
C = 4.11 * 121
C ≈ ₱498.31
Therefore, a pizza with an 11-inch radius should cost approximately ₱498.31.
To find out how much a pizza with an 11-inch radius should cost, we can use the concept of direct variation.
We are given that the cost of a pizza varies directly as the square of its radius. This means that if we double the radius, the cost will increase by a factor of four.
Here's how we can solve the problem step by step:
1. Set up a proportion to find the constant of variation:
Let's denote the cost of the pizza as C and the radius as r.
We know that C varies directly with the square of r. Therefore, we can write the equation:
C = k * r^2,
where k is the constant of variation.
2. Use the given information to find the value of k:
With the given information that a pizza with a 6-inch radius costs ₱148.00, we can substitute these values into our equation:
148 = k * 6^2.
Solve this equation to find the value of k:
k = 148 / (6^2).
k = 148 / 36.
k ≈ 4.1111.
3. Plug in the value of k to find the cost of a pizza with an 11-inch radius:
We want to find the cost of a pizza with an 11-inch radius, so we substitute r = 11 into our equation:
C = 4.1111 * 11^2.
C = 4.1111 * 121.
C ≈ ₱498.88.
Therefore, a pizza with an 11-inch radius should cost approximately ₱498.88.