Formula & Units
Write the formula for the volume of a rectangular prism.
V = l x w x h.
Find the volume of a prism that is 4 cm x 3 cm x 2 cm.
24 cm³.
The base area is 24 cm² and the height is 5 cm. Find the volume.
120 cm³.
Prism A is 4 x 2 x 1. Prism B is 2 x 1 x 3. They touch but do not overlap. Find the total volume.
14 cubic units
A student says the volume of a 5 x 4 x 2 prism is 11 because 5 + 4 + 2 = 11. What should the student do instead?
Multiply the dimensions: 5 x 4 x 2 = 40 cubic units.
What type of unit should be used for volume: linear, square, or cubic?
Cubic units.
Find the volume of a prism that is 7 ft x 5 ft x 3 ft.
105 ft³.
The base area is 36 ft² and the height is 4 ft. Find the volume.
144 ft³.
Prism A is 4 x 2 x 3. Prism B is 2 x 2 x 3. They touch but do not overlap. Find the total volume.
36 cubic units: 24 + 12.
A box has volume 96 cm³ and dimensions 8 cm x 4 cm x ?. Find the missing dimension.
3 cm.
In V = l x w x h, what does h represent?
Height
A prism has volume 144 in³, length 8 in, and width 3 in. Find the height.
6 in, because 8 x 3 x 6 = 144.
A prism has volume 210 cm³ and base area 35 cm². Find the height.
6 cm.
A step-shaped solid is split into prisms with volumes 40 ft³ and 24 ft³. Find the total volume.
64 ft³.
Choose whole-number dimensions with base area at least 30 ft² and volume less than 100 ft³. Give one valid answer.
Example: 6 ft x 5 ft x 3 ft. Base area = 30 ft²; volume = 90 ft³.
Write a volume formula that uses B for the area of the base.
V = B x h.
A prism has 5 equal layers with 18 unit cubes in each layer. What is its volume?
90 cubic units.
The base is 8 m by 6 m and the prism height is 3 m. Use base area first to find the volume.
Base area = 48 m²; volume = 144 m³.
A composite solid is made of a 6 x 3 x 2 prism and a 2 x 3 x 4 prism. Find the total volume.
60 cubic units: 36 + 24.
A prism has length 9 cm, width 4 cm, and volume 180 cm³. Find its height and explain how you know.
5 cm, because 9 x 4 = 36 and 180 ÷ 36 = 5.
Why is cm³ a better unit for volume than cm²?
Volume measures 3D space, so the unit is cubic; cm² measures area.
A prism is 5 x 6 x 4. Name THREE different multiplication expressions that equal its volume.
Examples: 5 x 6 x 4; 30 x 4; 20 x 6. Each equals 120.
A prism has volume 360 in³ and height 8 in. What is the area of its base?
45 in², because 360 ÷ 8 = 45.
Why should you avoid counting the same space twice when finding the volume of a composite solid?
Overlapping or repeated regions would make the total volume too large.
A rectangular prism has a base area of 54 m². Its volume must be less than 200 m³. What whole-number heights are possible?
1 m, 2 m, or 3 m. Heights 4 m or more give at least 216 m³.