Chapter 12.2, Problem 51SPR

To determine

Tofind:The option that give more cake for the money.

Answer to Problem 51SPR

Both the options give same quantity of cake for the money.

Explanation of Solution

Given information:

A bakery sells single layer mini-cakes that are 3 inches in diameter for $4 each and other cake with 9 inch diameter for $15. Both cakes are of same thickness.

Formulaused:

The volume of disk of diameter D thickness t is given by $V=$ area of the base $\times$ thickness that is $V\text{=π}{\left(\frac{D}{2}\right)}^{2}t\text{=}\frac{\text{π}{D}^{2}t}{4}$ .

Calculations:

Let us buy 9 mini-cakes that cost $36.

The volume of material of 9mini-cakes $V_m\text{=9}\times \frac{\text{π}{\left(3\right)}^{2}t}{4}\text{=}\frac{\text{81π}t}{4}$ inch³.

If webuy one 9- inch cake that cost $15.

The volume of material of one 9-inch cake $V_l\text{=1}\times \frac{\text{π}{\left(9\right)}^{2}t}{4}\text{=}\frac{\text{81π}t}{4}$ inch³, i.e., we get equalquantity of cake for the money.

Thus, both options give same quantity of cake for the money.

Conclusion:

Boththe options give same quantity of cake for the money.