Amount

[Guest]

To frost the top and sides of a 6 inch cake, enough is available. Determine amount needed to frost the top and sides of an 8 inch cake.

Both are round and 2 inches in height.


Both are a cylinder.

Radius of 6 inch: 3

Radius of 8 inch: 4

Not sure how to proceed.

[Guest]

Please reply, Thanks.

[Guest]

Please reply.

[Guest]

Since you’re frosting only the **top and sides** of the cake (not the bottom), you want the surface area of a cylinder without the base.

For a cylinder:

* Top area = $ \pi r^2$
* Side area = $2\pi rh$

So total frosting area is: $A = \pi r^2 + 2\pi rh$

For both cakes, height (h=2).

6-inch cake

Radius (r=3)

$A_6 = \pi(3^2) + 2\pi(3)(2) = 9\pi + 12\pi = 21\pi$

8-inch cake

Radius (r=4)

$A_8 = \pi(4^2) + 2\pi(4)(2)= 16\pi + 16\pi= 32\pi$

You need: $\frac{32\pi}{21\pi} = \frac{32}{21} \approx 1.52$

So the 8-inch cake needs about 1.52 times as much frosting as the 6-inch cake.

That means:

* about 52% more frosting, or
* multiply your 6-inch frosting recipe by 1.52.

[Guest]

Ok, Thanks.