Question

A cylindrical cake is made in a pan that has a diameter of 9 inches and a height of 1.5 inches. a) What is the total surface area of the cake?b)The cake is cut into 10 equal-sized wedges. What is the total surface area of the cake now?c) After the cake is cut, what percent of the cake's surface is covered with icing?d)Cake does not stay as moist after it has been cut into pieces. Use the surface area to explain this.

Answer 1

In this session we will focus on question a). Note that as the cake is made with a pan. the shape of the cake mostly the same as the one from the pan. So, we can assume that the cake has a diameter of 9 inches and a height of 1.5 inches too.

We want to calculate the surface area of a cylinder. Recall that we can think of a cylinder as the edge joined to two circles. So, the surface area of the cylinder is simply the sum of the area of both circles and the area of the edge

Recall that the area of a circle of radius r is given by the formula

`\pi r^2`

Since we have two circles, then the area asociated to the circles would be

`2\pi r^2`

In our case, we have that r is one half of the diameter of the cake, which would be 4.5 inches. So the area of both circles would be

`2\pi\cdot(4.5)^2=127.2345`

For the other part, note that it is a rectangle with the following dimensions

since the base is 2*pi* r and the height is h then the area of this portion would be

`2\cdot\pi\cdot r\cdot h`

so, in our case we have r=4.5 inches and h=1.5 inches. So we have that

`2\cdot\pi\cdot r\cdot h=9\cdot\pi\cdot1.5=42.4115`

so the total surface area of the cake would be

`2\cdot\pi\cdot r^2+2\cdot\pi\cdot r\cdot h=169.646`

so the total surface area of the cake is 169.646 squared inches