SOLUTION: Hi, I'm in geometry and I'm struggling with volume and surface area. I have a worksheet with word problems, which are not my forte. Anyways, the problem is stated exactly as follow

Algebra ->  Surface-area -> SOLUTION: Hi, I'm in geometry and I'm struggling with volume and surface area. I have a worksheet with word problems, which are not my forte. Anyways, the problem is stated exactly as follow      Log On


   

Question 187461: Hi, I'm in geometry and I'm struggling with volume and surface area. I have a worksheet with word problems, which are not my forte. Anyways, the problem is stated exactly as follows: "At Cakes R Us, it is possible to buy round cakes in different sizes. The smallest cake has a diameter of 8 inches and height of 4 inches and requires 3 cups of batter. Another similar round cake has a diameter of 13 inches. How much batter would this cake require?" By the way, this problem is not in my book. It's on a worksheet my teacher gave me. Thanks so much.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
At Cakes R Us, it is possible to buy round cakes in different sizes. The
smallest cake has a diameter of 8 inches and height of 4 inches and requires
3 cups of batter. Another similar round cake has a diameter of 13 inches.
How much batter would this cake require?"
:
This would be based on the ratio of the volumes of the two cakes
cancel out pi, and height
small+cake%2Flarge+cake = %28pi%2A8%5E2%2A4%29%2F%28pi%2A13%5E2%2A4%29 = 64%2F169
:
Let x = amt of batter needed for the large cake
;
64%2F169 = 3%2Fx
Cross multiply
64x = 3 * 169
:
64x = 507
:
x = 507%2F64
x = 7.9 cups