Question

A small pizza has an 8-in. Diameter a large pizza has a 15-in. Diameter. The pizzeria charges the same price per square inch for both pizzas. If the small pizza cost $7, how much does the large pizza cost?

Answer 1

The cost of large pizza is $24.62, a small pizza has an 8-in. diameter a large pizza has a 15-in. diameter the pizzeria charges the same price per square inch for both pizzas and the small pizza cost $7.

Step-by-step explanation:

The given is,

                A small pizza has an 8-inches in diameter

                A large pizza has a 15-inches in Diameter

                The small pizza cost $7

Step:1

                Area of smaller pizza,

                                        $Area, A_{S} = \pi r^{2}$...................................(1)

                 Where, r - Radius of small pizza

                 From given, $r=\frac{d}{2}$

                                         $= \frac{8}{2}$

                                       r = 4 inches

                  Equation (1),

                                    $A_{S} = \pi 4^{2}$

                                          $=(3.14)(16)$                             ( ∵ $\pi$=3.14 )

                                          $= 50.24$ Square inches

Step:2

              Area of smaller pizza,

                                        $Area, A_{L} = \pi r^{2}$...................................(1)

                 Where, r - Radius of small pizza

                 From given, $r=\frac{d}{2}$

                                         $= \frac{15}{2}$

                                       r = 7.5 inches

                  Equation (1),

                                    $A_{S} = \pi 7.5^{2}$

                                          $=(3.14)(56.25)$                             ( ∵ $\pi$=3.14 )

                                          $= 176.625$ Square inches

Step:3

            Cost of pizza per square meter,

                                                $= \frac{Cost of small pizza}{Area of small pizza}$

                                                $=\frac{7}{50.24}$

                                                = $ 0.1393 per square meter

                $Cost of Larger pizza = Area of Larger pizza$ × $Cost per square meter$

                                                $= (176.625)(0.139331)$

                                                = $24.62

Result:

          The cost of large pizza is $24.62, a small pizza has an 8-in. diameter a large pizza has a 15-in. diameter the pizzeria charges the same price per square inch for both pizzas and the small pizza cost $7.