Volume in the Real World Small Group Problems - KEY
1. Gomer delivers muffins for the Muffin-O-Matic muffin company. Each muffin is
packed in its own little box. An individual muffin box has the shape of a cube,
measuring 3 inches on each side. Gomer packs the individual muffin boxes into a
larger box. The larger box is also in the shape of a cube, measuring 2 feet on each
side. How many of the individual muffin boxes can fit into the larger box?
1. Find the volume of the individual muffin boxes: V = 3 · 3 · 3 or 27in3
2. Find the volume of the larger box: V = 2 · 2 · 2 or 8 ft3
3. You must convert cubic feet to cubic inches so that the measurements are
compatible. To do this we must figure out how many cubic inches are in a cubic
foot. There are 12 inches in a foot so to find the cube of 12 I multiply 12 · 12 · 12
which equals 1728; so there are 1728 in3 in a cubic foot.
4. Find the volume of the larger box in cubic inches: 8 ft3 · 1728 in3 = 13,824 in3
5. Find how many smaller boxes can fit into the larger box by dividing the volume of
the larger box by the volume of the smaller box: 13824 ÷ 27 = 512 individual boxes
2. Suppose that a rectangular aquarium that is 12 inches long, 8 inches wide and 8
inches high provides enough room to safely house 6 guppies. Assuming that the
number of guppies that can be safely housed depends upon the size of the
aquarium, how many guppies can be safely housed in an aquarium that is 24 inches
long, 16 inches wide and 16 inches high?
1. Find the total volume safe for housing 6 guppies: V= lwh = 12 · 8 · 8 = 768 in3
2. Find the volume of the aquarium: V = lwh = 24 · 16 · 16 = 6144 in3
3. Divide the total volume by the volume needed for 6 guppies to see how many
sets of 6 guppies you can fit into the tank: 6144 ÷ 768 = 8
4. So, 8 · 6 = 48 guppies
Volume in the Real World Small Group Problems - KEY
3. People living in Florida sometimes find that the water in their swimming pools
becomes uncomfortably warm during the summer months. This situation can be
rectified by adding ice cubes to the pool. The following authentic formula can be
used to determine the approximate number (N) of 5-pound bags of ice required to
reduce the temperature of a pool by D degrees Fahrenheit if the volume of the pool
is V cubic feet: N = 0.06125·D·V. Gomer’s pool is roughly rectangular in shape, with a
length of 50 feet, width of 20 feet and average depth of 5 feet. How many bags of
ice will be required to reduce the temperature of the pool by 10°?
1.
2.
3.
4.
Find the volume of the pool: V = lwh = 50 · 20 · 10 = 5000 ft3
Use the formula: N = 0.06125 · D · V
Replace the variables: N = 0.06125 · 10 · 5000
And solve: N = 3,062.5 bags of ice
4. Gomer is digging a hole for a rectangular swimming pool measuring 38 feet long by
22 feet wide by 8 feet deep. How much water will the swimming pool hold, assuming
that 1 cubic foot = 7.5 gallons.
1. Find the volume of the pool: V = lwh = 38 · 22 · 8 = 6688 ft3
2. Divide cubic feet by 7.5 to convert to gallons: 6688÷7.5 = 892 gallons
5. The pedestal on which a statue is raised is a rectangular concrete solid measuring 9
feet long, 9 feet wide and 6 inches high. How much is the cost of the concrete in the
pedestal, if concrete costs $70 per cubic yard?
1. Convert all measurements to yards: 9 feet = 3 yards and 6 inches = 1/6 yard
2. Find the volume of the pedestal: V = lwh = 3 · 3 · 1/6 = 1 ½ yd3
3. Multiply the volume by $70: 1.5 · 70 = $105.00
Volume in the Real World Small Group Problems - KEY
6. Cube-shaped boxes will be loaded into the cargo hold of a truck. The cargo hold of
the truck is in the shape of a rectangular prism. The edges of each box measure 2.50
feet and the dimensions of the cargo hold are 7.50 feet by 15.00 feet by 7.50 feet, as
shown below.
What is the volume, in cubic feet, of each box?
Cargo hold: V=lwh = 7.5 · 15 · 7.5 = 843.75 ft3
Small box: V = lwh = 2.5 · 2.5 · 2.5 = 15.625 ft3
How many boxes will completely fill the cargo hold of the truck?
Divide the volume of the cargo hold by the volume of the small box:
843.75 ÷ 15.625 = 54 boxes will completely fill the cargo hold
7. A construction crew is repairing a 101ft-long section of a highway. The road is 9ft
wide, and the concrete must be poured to the depth of 6in. How many cubic feet of
concrete will be required for the repair?
1.
2.
Convert all measurements to feet: 6in. = ½ ft.
Find the volume of the road: V = lwh = 101 · 9 · ½ = 454 ½ ft3
Volume in the Real World Small Group Problems - KEY
8. Emma Stone is managing a storage business. She has a small unit available with the
dimensions of the figure below. Each standard box is ½ m. on each side.
How many boxes will fit in the available space?
1. Find how many boxes will fit on each edge:
5/2 = 5 boxes
3/2 = 3 boxes
3/2 = 3 boxes
5 · 3 · 3 = 45 boxes
What is the total volume of the space?
1. Find the volume of the storage unit:
V= lwh = 3/2 · 3/2 · 5/2 = 45/8 m3
Method 2:
Find the volume of the small box:
V = lwh = ½ · ½ · ½ = 1/8 m3
and then divide into the volume of the storage unit:
45/8 ÷ 1/8 = 45/8 · 1/8 = 45 boxes
9. A trailer is 9 feet wide and 40 feet long. How tall would it need to be to hold 3,240
cubic feet?
1. Fill in the volume formula with provided numbers: V = lwh = 3240 = 40 · 9 · h
2. Solve for h: 3240 = 360h
3240/360 = 360h/360
9 =h so 9 ft.
Volume in the Real World Small Group Problems - KEY
10. Mr. Sanchez filled a container 7 feet long, 4 feet wide, and 3 feet high with apples.
He is looking for another container with 2.5 times as many apples. What is the
volume of the container he is looking for?
1. First find the volume of the original container: V = lwh = 7 · 4 · 3 = 84 ft3
2. Figure out what the volume would be if it was 2.5 times as big: 84 · 2.5 = 210 ft3
What could the dimensions of the new container be?
Use the volume formula to try different numbers to determine the correct
volume: V = lwh ex. 210 = 6 · 7 · h
210 = 42h
210/42 = 42h/42 5 = h
11. A store keeps about 150 boxes of paper in stock. If each box has a length of 17
inches, a width of 11 inches, and a height of 9 inches, about how many cubic feet of
storage space does the store need for the paper? Round your answer to the nearest
cubic foot.
1. Find the volume of the box: V = lwh = 17 · 11 · 9 = 1683 in3
2. Find the total volume for all 150 boxes: 1683 · 150 = 252450 in3
3. You must convert cubic feet to cubic inches so that the measurements are
compatible. To do this we must figure out how many cubic inches are in a
cubic foot. There are 12 inches in a foot so to find the cube of 12 multiply 12 · 12
· 12 which equals 1728; so there are 1728 in3 in a cubic foot.
4. Convert the volume in cubic inches into cubic feet: 252450 ÷ 1728 = 146 ft3
12. A cube shaped pool is half full of water. If the water is 36 inches deep, how much
would the water in the pool weigh if the pool were filled to the brim? (1 cubic foot
weighs 56 pounds)
1. Find the side dimension if the cube is full: 36 · 2 = 72 in
2. Find the volume of the cube: V = s3 = 72 · 72 · 72 = 373248 in3
3. You must convert cubic feet to cubic inches so that the measurements are
compatible. To do this we must figure out how many cubic inches are in a cubic
foot. There are 12 inches in a foot so to find the cube of 12 multiply 12 · 12 · 12
which equals 1728; so there are 1728 in3 in a cubic foot.
4. Convert from cubic inches to cubic feet: 37324÷1728 = 216 ft3
5. Convert to pounds: 216 · 56 = 12,096 pounds
Volume in the Real World Small Group Problems - KEY
13. Peter wants to put 5 fish in his aquarium. Three of the fish need 1/4 of a cubic foot of
water apiece, and two of them need 1/3 of a cubic foot of water. The dimensions of
Peter’s aquarium are 1’ x 1’ x 2’. Does he have room to add another fish that needs
2/3 of a cubic foot of water? Assume that the aquarium is filled to the top.
1.
Determine how much room his current fish need:
Fish 1: ¼ ft3
Fish 3: ¼ ft3
Fish 2: ¼ ft3
Add them up:
Fish 4: 1/3 ft3
Fish 5: 1/3 ft3
¼ + ¼ + ¼ + 1/3 + 1/3 =
3/12 + 3/12 + 3/12 + 4/12 + 4/12 =
17/12 = 1 5/12 ft3 used
2. Determine the volume of the tank: V = lwh = 1 · 1 · 2 = 2 ft3
3. The last fish needs 2/3 ft3 which converts to 8/12 to add to 1 5/12 = 2 1/12 which is
greater than the volume of the fish tank so no, he cannot get another fish.