Volume Basics
What is volume?
The amount of three-dimensional (3D) space that an object occupies. Think of it as how much "stuff" can fit inside something.
What is the volume of a rectangular prism with dimensions 3 cm, 4 cm, and 5 cm?
3cmx4cmx5cm=60 cubic cm
A box has a length of 6 cm, a width of 2 cm, and a height of 4 cm. What is its volume?
Which is greater: a volume of 10 cm³ or 8 cm3?
A volume of 10 cm³ is greater than 8 cm³.
A prism has dimensions 7 × 3 × 2. What is the volume?
42 cubic units
How do you find the volume of a cube?
You multiply the length of one side by itself twice, or side×side×side. Since all sides of a cube are equal.
If a rectangular prism has a volume of 60 cm³ and a length of 5 cm, what is the height if the width is 3 cm?
60/5=12 and 12/3=4 so the height of the rectangular prism is 4cm.
If a container holds 45 liters of water, how many cubic centimeters does it hold? (1 liter = 1000 cm³)
One liter is equal to 1000cm3, so 45 liters would be 45×1000=45,000cm3
Compare: A prism with dimensions 4 × 3 × 2 vs. 6 × 2 × 2.
They are equal, both 24 cubic units
A compound figure is made of a rectangular prism with a volume of 36 cm³ and a cube with a volume of 8 cm³. What is the total volume?
The total volume is the sum of the individual volumes: 36cm3+8cm3=44cm3
What units are used to measure volume?
Volume is measured in cubic units.
How many unit cubes fit into a rectangular prism with a volume of 24 cm³?
24 unit cubes
A fish tank measures 2 feet long, 1 foot wide, and 1 foot tall. What is the volume in cubic feet?
The volume is 2 ft x 1 ft x 1ft = 2 ft3
A cube with side 5 vs. a rectangular prism 10 × 2 × 2
The cube is greater with 125 cubic units compared to 40 cubic units
How would you find the volume of an irregular figure made of unit cubes?
Count them.
What is the formula for calculating the volume of a rectangular prism?
V=lxwxh or V=area of the basexh
Write an expression for the volume of a rectangular prism with a length of 2in, width of 4in, and height of 6in.
2inx4inx6in=48 cubic in
If a toy is made up of 10 unit cubes, what is the volume of the toy if each cube has a volume of 1 cm³?
Since each unit cube has a volume of 1cm3, the total volume of the toy made of 10 cubes is 10×1cm3=10cm3.
Which has more volume: A prism 12 × 2 × 2 or 8 × 3 × 2?
They are the same, 48 cubic units
If the volume of a cube is 64 cm³, what is the total volume of 5 of the same cubes?
The total volume of 5 cubes would be 5×64cm3=320cm3
Explain how volume relates to multiplication.
Volume relates to multiplication because it's the product of three dimensions: length, width, and height. It's like finding the total number of unit cubes that can fill a space by multiplying the number of cubes along each dimension.
If you combine two rectangular prisms each with a volume of 15 cm³, what is the total volume?
15 cm³+15 cm³=30 cm³
Sarah has a box that is 3 cm by 4 cm by 5 cm. If she fills it with water, how much water can it hold?
The volume of the box is 3cm×4cm×5cm=60cm3. So, if she fills it, it can hold up to 60 cm³ of water.
Which would hold more water: a tank 5 × 4 × 3 or a tank 6 × 2 × 4?
The first tank would hold more water, 60 cubic units compared to 48 cubic units
A pool is 20 m × 8 m × 2 m. If it’s only half filled, what is the volume of water inside?
160 cubic m