Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 6 Measurement
Problem
Solution
1) A box has volume 24 cubic feet. It has a length of 3 feet and a width of 2 feet. If the width is increased by 2 feet, by how much does the volume increase? 1. Compute the height of the box given it's volume, length and width =
    24 = 3 x 2 x h
    6h = 24; h = 4 ft.
2. Add 2 feet to the width and compute the volume given the above information.
    new volume = 3 x 4 x 4 = 48 cu. ft.
3. Subtract the original volume from this = 48 - 24 =
    24 cu. ft.
2) Trevor and Debby are designing a fort. They notice that if they increase the length of the floor by 2 feet then the floor area will increase by 12 square feet. If they increase the width by 3 feet then the floor area will increase by 24 square feet. If they do both and increase the length by 2 feet and the width by 3 feet, by how much will the area increase? 1. If the floor area increases by 12 sq. ft. when 2 feet is added to the length, then the width was 12/2 = 6 feet.
2. If the floor area increases by 24 sq. ft. when 3 feet are added to the width, then the length was 24/3 = 8 feet.
3. The original floor is 8 x 6 = 48 sq. ft.
4. The new floor is 10 x 9 = 90 sq. ft.
5. Subtract the old area from this = 42 sq. ft.
3) Jori, Tina, and Lateisha are going to be paid $80 for cleaning up Mr. Roger's neighborhood. They each worked 5 hours except Jori who was 30 minutes late. What is Lateisha's fair share of the money? Mr. Roger is generous and rounds up to the nearest dollar. 1. Compute the total hours worked by all three =
    5 x 2 + 4.5 = 14.5 hours.
2. Divide $80 by this to get the pay per hour = $5.517
3. Compute Lateisha's share as her number of hours actually worked x the hourly rate = 5 x 5.517 = 27.585
4. Round up to the nearest dollar = $28

Problem
Solution
4) Ms. Creeley's class is doing a canned food drive. All the cans will be placed in a large cylindrical barrel that Ally and Joe are going to decorate like a can of stew. The barrel has a radius of 18 inches and is 3 feet high. They plan to first cover it in sheets of 9 inch by 14 inch construction paper. The art teacher will give them the construction paper only if they tell her what is the fewest number sheets they will need. How many sheets will they need if they cover only the sides of the barrel? Remember they can only get whole sheets. 1. Convert the height of the barrel to inches = 36
2. Compute the circumference of the barrel = 113.1 in.
3. Compute the area of the sides of the barrel =
    36 x 113.1 = 4071.6 sq. in.
4. Compute the area in inches of 1 sheet of construction paper =
    9 x 14 = 126 sq. in.
5. Divide the barrel area by the area of a single sheet =
    4071.6 / 126 = 32.31
6. Round up to the next number of sheets = 33 sheets.

5) Mr. Troy is transporting bars of gold in an elevator that will hold a maximum weight of 500 pounds. He weighs 180 pounds and his cart weighs another 15 pounds. Each bar of gold weighs about 27.4 pounds. He tries to maximize the number of bars he can take in each trip without going over the maximum elevator weight. On this day one bar is worth $623.80. What's the value of the gold in the elevator with Mr. Troy? 		1. Subtract Mr. Troy's weight and the cart weight from the maximum weight the elevator will hold =
    500 - 180 - 15 = 305 pounds.
2. Divide this by the weight of a bar of gold =
    305 / 27.4 = 11.13 = 11 bars.
3. Multiply this by the cost of 1 bar =
    11 x 623.80 = $6861.80