A company is trying to decide between a spherical- or cube-shaped tree ornament. Which ornament would require less paint?

• A spherical ornament with a diameter of 2.48 inches
• A cube-shaped ornament with a side length of 1.80 inches

Step 1. Sketch a diagram and label with the appropriate measurements. What are the relevant formulas we might use for this problem?

Explanation:

The relevant formulas for a sphere are:

SA = 4r²

V = (4/3)r³

The relevant formulas for a cube are:

SA = 6s²

V = s³

Because the ornaments are being painted, we are concerned with surface area for each.

Step 2. Identify all the known values you can substitute into the surface area formula.

Sphere ornament:

SA = ____________

r = ____________

Cube ornament:

SA = ____________

S = ____________

Explanation:

Sphere ornament:

SA = unknown

r = 1.24 inches

Cube ornament:

SA = unknown

S = 1.8 inches

Step 3. Substitute into the surface area formula for both spheres.

Sphere ornament: ________

Cube ornament: _________

Explanation:

Sphere ornament: SA = 4(1.24)2 = 19 square inches

Cube ornament: SA = 6 (1.8)2 = 19 square inches

Step 4. Use your calculations to answer the original question in bold.