Question

The cost of a pizza varies directly as the square of its radius. If

a pizza with a 6-inch radius costs $8.00, how much should a pizza

with an 11-inch radius cost?

​

Answer 1

SOLUTION

GIVEN

• The cost of a pizza varies directly as the square of its radius.

• A pizza with a 6-inch radius costs $ 8.00,

TO DETERMINE

The cost of a pizza with an 11-inch radius

EVALUATION

Let $ y be the cost of a pizza of radius r inch

Now it is given that the cost of a pizza varies directly as the square of its radius.

$\sf{y \: \propto \: {x}^{2} }$

$\implies \sf{y = k {x}^{2} }$

Where k is a non zero real number

Now y = 8 when x = 6

$\sf{ \implies \: 8 = k \times {6}^{2} }$

$\sf{ \implies \: 8 = 36k }$

$\displaystyle \sf{ \implies \: k = \frac{8}{36} }$

$\displaystyle \sf{ \implies \: k = \frac{2}{9} }$

$\displaystyle \sf{ \implies \: y= \frac{2}{9} {x}^{2} }$

Now for x = 11 we have

$\displaystyle \sf{ \: y= \frac{2}{9} \times {(11)}^{2} = \frac{242}{9} }$

Hence the required cost is $ $\displaystyle \sf{ \: \frac{242}{9} }$

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