Lisa glued two pieces of wood together to make the letter L in her art class. She plans to paint all sides of it purple, including the base.
Note: Figure is not drawn to scale.
The longer piece of wood has dimensions of 1 inch by 1 inch by 6 inches. The shorter piece of wood has dimensions of 5 inches by 1 inch by 1 inch. How many square inches of purple paint will Lisa use to paint her letter L?
A.
48 square inches
B.
47 square inches
C.
35 square inches
D.
46 square inches
First, let's calculate the surface area of each piece of wood:
Longer piece of wood:
- 2 sides with dimensions 1 inch by 6 inches = 2 * 1 * 6 = 12 square inches
- 2 sides with dimensions 1 inch by 1 inch = 2 * 1 * 1 = 2 square inches
- 1 side with dimensions 6 inches by 1 inch = 6 * 1 = 6 square inches
Total surface area for longer piece = 12 + 2 + 6 = 20 square inches
Shorter piece of wood:
- 2 sides with dimensions 5 inches by 1 inch = 2 * 5 * 1 = 10 square inches
- 2 sides with dimensions 1 inch by 1 inch = 2 * 1 * 1 = 2 square inches
- 1 side with dimensions 5 inches by 1 inch = 5 * 1 = 5 square inches
Total surface area for shorter piece = 10 + 2 + 5 = 17 square inches
Now, total surface area for both pieces of wood = 20 + 17 = 37 square inches
Since Lisa is painting all sides of the letter L, this means she needs to paint the top, bottom, and all sides of both pieces of wood. This means she will need to paint the combined surface area of both pieces, so the total area to be painted is 2 * 37 = 74 square inches.
However, the base of the letter L will not need to be painted in addition to the sides and top, so we need to subtract the area of the base (6 inches by 5 inches = 30 square inches) from the total area calculated above: 74 - 30 = 44 square inches.
Therefore, Lisa will use 44 square inches of purple paint to paint her letter L.
Therefore, the closest answer option is D. 46 square inches.