Question

A birthday cake has a diameter of 9 inches. A wedding cake has a diameter of 14 inches. What is thedifference in area between the top surfaces of the two cakes?

Answer 1

90.32 square inches

Step-by-step explanation

Step 1

the area of the circle is given by:

`\text{Area}=(\pi)/(4)\cdot diameter^2`

Step 2

find the areas

birthday cake

`\begin{gathered} \text{Area}_b=(\pi)/(4)\cdot9^2 \\ \text{Area}_b=(81\pi)/(4) \\ \text{Area}_b=(254.46)/(4) \\ \text{Area}_b=63.61\text{ square inches} \end{gathered}`

Now, the wedding cake

`\begin{gathered} \text{Area}_w=(\pi)/(4)\cdot14^2 \\ \text{Area}_w=(\pi)/(4)\cdot196\text{ square inches} \\ \text{Area}_w=49\cdot\pi\text{ square inches} \\ \text{Area}_w=153.93\text{ square inches} \end{gathered}`

Step 3

finally, find the difference

`\begin{gathered} \text{difference}=153.93\text{ square inches-63.61 inches} \\ \text{difference}=90.32 \end{gathered}`

so, the answer is 90.32 square inches