SOME MATHEMATICAL PROBLEMS WITH SOLUTION | SCIENCE TUTOR

SOME MATHEMATICAL PROBLEMS WITH SOLUTION | SCIENCE TUTOR

1. Anne has two containers for water: A rectangular plastic pitcher with a base of 16 square inches, and a cylindrical vase with a radius of 2 inches and a height of 11 inches. If the rectangular pitcher is filled with water 9 inches from the bottom, and Anne pours the water into the vase without spilling, which of the following will be true?

a. The cylinder will overflow.

b. The cylinder will be exactly full.

c. The cylinder will be filled to an approximate level of 10 inches.

d. The cylinder will be filled to an approximate level of 8 inches.

2. Faleena was given a 110-question homework assignment. On Friday night, she did 1/5 of the assignment. On Saturday, she finished 1/4 of the remaining questions. On Sunday, she did another 1/3 of the remaining questions. How many questions does Faleena have left?

a. 23

b. 32

c. 44

d. 51

3. Adam collected the following amounts of change from under his living room furniture: 0.24, 0.75,

0.89, and 1.27. How much money did he find altogether?

a. $315.00

b. $31.50

c. $3.15

d. $0.315

4. Six students agree to equally divide the cost of materials needed for a project. If the total cost of

materials is $27.90, how much money does each student need to pay?

a. $4.50

b. $4.65

c. $6.75

d. $6.80

SOLUTIONS

1. a. Begin by calculating the volume of the water. Use the formula for the volume of a rectangular

solid to calculate the volume of the water: V = Ah = lwh. The area of the base is 16

inches2 and the height of the water is 9 inches, so to get the volume of the water in the

pitcher you plug these known measures into the formula and solve:

V = Ah = lwh

V = (16 in2)(9 in)

V = 144 in3

So, the volume of the water is 144 in3.

Next, calculate the volume of the vase. The formula for the volume of a cylinder is V = Ah

or V = πr2h. So, you plug in the measures and solve:

V = πr2h

V = π(2)2(11)

V = π(4)(11)

V = π(44)

V = 138.16

So the volume of the vase is about 138 cm3, and this volume is smaller than the volume

of water in the pitcher, so the vase will overflow if Anne tries to fill it with all the water in

the pitcher.

2. c. When you are asked to take a fraction of another number, you are being asked to multiply the number by that fraction. Here’s what Faleena does each day:

3. c. To solve this problem correctly, you must be sure that the decimal points are lined up correctly.

Now you are ready to add:

0.24

0.75

0.89

+1.27

3.15

So, Adam found $3.15. 

4. b. Divide the total amount ($27.90) by six students. To do this, you need to first set up the

division problem. Begin by writing the decimal point in the answer portion of the division

problem. It should go just above the decimal point in the problem. Now you are ready to

divide:

Your final answer is $4.65.