SOLUTION: the cost of a pizza varies directly as the square of its radius. If a pizza with a 6 inches' radius cost 180, how much should a pizza with an 11 inches' radius cost?

Question 1199119: the cost of a pizza varies directly as the square of its radius. If a pizza with a 6 inches' radius cost 180, how much should a pizza with an 11 inches' radius cost?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
y = kx is the direct variation equation.
the cost of a pizza varies directly as the square of its radius.
the formula becomes y = k * r^2
r is the radius of the pizza
x = r^2
y is the cost of the pizza.
when the radius is 6 inches, the pizza costs 180.
formula becomes 180 = k * 6^2 = k * 36
solve for k to get k = 180 / 36 = 5.
k always stays the same in that equation.
when the pizza radius is 11 inches, the formula becomes:
y = 5 * 11^2 = 605.
that's the cost of the pizza with 11 inch radius.

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

The other tutor solves the problem by finding the constant of proportionality to find a formula relating the radius of the pizza and its cost. That would be a good path to the solution if you were going to use the formula multiple times to find the costs of several pizzas of different sizes.

But that is more work than necessary if, as in this case, you only need to find the cost of one other pizza.

The cost varies directly as the square of the radius of the pizza, so you can find the cost of the larger pizza by multiplying the cost of the small pizza by the ratio of the squares of the two radii.

ANSWER: 605

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