HW B: Advanced Volume Problems
1.
After a maximum number of 5-cm plastic cubes are packed into a rectangular box measuring 33
cm by 22 cm by 20 cm, what is the volume of the space left in the box?
2.
Air is pumped into a wheel at the rate of 405 cm3 per minute. At the same time, 45 cm3 of air is
leaking through a hole every minute. If the wheel has a capacity of 1620 cm3, how many minutes will it
take to fill the remaining space in the wheel after 2/3 of the wheel has been filled with air?
3.
The volume of a wooden cuboid is 5184 cm3. It can be cut exactly into either 3-cm cubes or 2-cm
cubes. The ratio of the length of the cuboid to its breadth to its height is 4 : 3 : 2. What are the
dimensions of the cuboid?
4.
The length of cube B is 3 times the length of cube A. How many percent larger is the volume of
cube B than that of cube A?
5.
A cuboid has a rectangular front face with an area of 48 cm2. If the side face is a square and the
ratio of the length of the cuboid to its width is 4 : 3, what is the volume of the cuboid?
6.
A cubical container was completely filled with oil. All the oil was then poured into a larger
rectangular container, 30 cm by 10 cm by 24 cm, filling 81% of it. What is the length of the cubical
container?
7.
A rectangular tank was 14/15 filled with 5.6 litres of water. When 25 stones were put into the
tank, 180 cm3 of water from the tank overflowed.(a) What was the volume of each stone? (b) What
percentage of the capacity of the tank was the volume of water that overflowed?
8.
When a rectangular piece of brick, 22 cm by 10 cm by 5 cm, is placed in a square-based
rectangular container that is 6% filled with water, half of the brick is immersed in the water. If the
length of the container is 25cm, what is the capacity of the container in litres?
9.
The water in a rectangular tank reaches the brim after a number of identical cubes are put in.
when one of the cubes is removed, the water level drops by 0.5cm, leaving 98% of the capacity of the
tank filled. If the volume of the water drops to 88% of the capacity of the tank after all the cubes are
removed, leaving only 9504cm3 of water in the tank, find (a) the number of cubes that are put in the
tank initially, (b) the length of each cube.
10.
A company wants to reduce the height of each of its rectangular cartons by 20% and to increase
the width. The company decides not to change the length and width are in the ratio 5 : 3, by how many
percent must the company increase the width of each carton, if the volume of each new carton is to
remain unchanged at 1200cm3 ?
1.
Step 1 : 33 /5 = 6 R 3
Step 2 : 22 /5 = 4 R 2
33 - 3 = 3
3 x 22 x 20 = 1320
2 x 30 x 20 = 1200
Step 3 : 1320 + 1200 = 2520 cm3
The volume of the space left in the box is 2520cm3
2.
This is mathematics and not science, so presume the air cannot be compressed.
Step 1 : 1620 x 2/3 = 1080
1620 - 1080 = 540
Step 2 : 405 - 45 = 360
Step 3 : 540 / 360 = 1.5
It will take 1 minute and 30 seconds to fill the remaining space in the wheel.
3.
2 cm = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26
3 cm = 3, 9, 12, 15, 18, 21, 24, 27, 30
2cm and 3cm have the common number of 12, 18 and 24.
12 x 18 x 24 = 5184 cm3
The dimensions of the cuboid are 12cm by 18cm by 24cm.
4.
A = 1 x 1 x1 = 1cm3
B = 3 x 3 x 3 = 27cm3
27 - 1 = 26cm3
26 /1 x 100% = 2600%
The volume of cube B than that of cube A is 2600% larger.
5.
Front face : 4 : 3 = 4 x 3 = 12
8 x 6 = 48 therefore length = 8cm and width = 6cm
Side face is a square, therefore the side is 6cm
8 x 6 x 6 = 288 cm3
The volume of the cuboid is 288cm3