NGA Classroom: Counting on Art: Student Activity: Sugary Shapes

Student Activity: Sugary Shapes (6–8 grade)

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California artist Wayne Thiebaud painted Cakes in 1963.

Read Ten Things about Thiebaud—you'll learn all about the artist.

Most of the cakes shown are the same geometric solid, a cylinder.

Solid shapes such as cylinders have volume. In this case, it is the amount of cake inside.

Wayne Thiebaud, Cakes, 1963

Let's focus on the Valentine cake:

The baker sells it as a 10-inch cake. Which part of the cake measures 10 inches?

Roll the mouse over the cake for a hint.

How can we calculate the amount of frosting on the cake?

First, try to estimate the amount of frosting you think it will take to ice the cake. Here are your choices: 12 square inches, 50 square inches, 98 square inches, or 222 square inches. This is how to figure the answer:
The formula for the surface area of a cylinder is: 2(pi)(r²) + 2(pi)(r)(h),
but the formula for the cake is: pi(r²) + 2(pi)(r)(h)

Why are they different? The cake is a cylinder, but the bottom is not frosted; so you only need to include the surface area of the top (so you don't need to double pi(r²).

Use what you know about the cake to calculate the surface area. Then select your answer on the right.

12 square inches of frosting
50 square inches of frosting
98 square inches of frosting
222 square inches of frosting

Doesn't that sound like a lot of frosting for one cake? If you have ever frosted a cake, you know it takes only a cup or two of frosting to cover its surface. It is amazing that those cups contain frosting to cover several hundred square inches!

Use what you have learned to calculate the volume and surface area of this 8" cake. It is 4" high.

Remember:
V = pi(r²)(h)
SA = pi(r²) + 2(pi)(r)(h)

See solution

All images on page: Wayne Thiebaud, Cakes, 1963

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