Question

A bakery offers a small circular cake with a diameter of 8 inches. It also offers a large circular cake with a diameter of 24 inches. Complete the explanation for whether the top of the large cake has three times the area of that of the small cake.

Answer 1

Large cake:
24÷2=12
12 is the radius of the large cake.
12×12×3.14=452.16

Small cake:
8÷2=4
4 is the radius of the small cake.
4×4×3.14=50.24

452.16÷3=150.72
So, The area of the large cake is not three times the area of the small cake.

Answer 2

We must find the area of each cake's top.

Formula for area of a circle:


`A = \pi r^(2)` where r is the radius.

small cake:
Plug in 4 for r because the radius is 4. (They give us the diameter, which is 8, and the radius is half that)


`A = \pi 4^(2)`

A = 16π

big cake:
Repeat the process:
Plug in 12 for r because the radius is 12. (They give us the diameter, which is 24, and the radius is half that)


`A = \pi 12^(2)`

A = 144π

So our two radii are 144π and 16π.
The large cake's top is not 3 times the area of the small cake's.

This makes sense because you are squaring the radius, which makes the fact that the larger cake's diameter is triple the smaller cake diameter irrelevant.

Hope this helped! ^-^