Question

Tom baked 2 cakes using a circular cake pan of diameter 10 inches. He plans to make a layered cake with one cake on top of the other with frosting only in between the two cakes and on top of the second cake. Maria baked 3 cakes using a circular cake pan of diameter 6 inches. She plans to make a layered cake with one cake on top of the other and frosting only in between the cakes and on top of the third cake. The height of frosting in both their cakes is the same.

Who requires more frosting?

Maria. She has to frost an area of 56.52 square inches, and Tom has to frost an area of 31.40 s

Answer 1

these are the choices:
Maria. She has to frost an area of 56.52 square inches, and Tom has to frost an area of 31.40 square inches.

Tom. He has to frost an area of 157 square inches, and Maria has to frost an area of 84.78 square inches.

Maria. She has to frost an area of 339.12 square inches, and Tom has to frost an area of 157 square inches.

Tom. He has to frost an area of 62.8 square inches, and Maria has to frost an area of 56.52 square inches.

Answer 2

Do you know the formula for the area of a circle?

Answer 3

yes it is \[\pi \times r ^{2}\]

Answer 4

Tom's cake has an area of twice the circular area of his cake to have frosting. So the frosted area is
\[2\pi \times 5^{2}=?\]

Answer 5

thats 157

Answer 6

so the answer is the 2nd choice?

Answer 7

"Tom. He has to frost an area of 157 square inches, and Maria has to frost an area of 84.78 square inches."

Answer 8

Right! 157 square inches of frosting is needed for Tom's cake. There are two choices with this value so better work out the area of frosting for Maria's cake which is
\[3\pi \times 3^{2}=?\]

Answer 9

84.78

Answer 10

Well done! You've got it :)

Answer 11

thanks :)

Answer 12

You're welcome :)