Volume Basics
What is volume?
The amount of space inside a 3D object.
What is surface area?
The total area of all faces of a 3D object.
Name a 3D shape with 6 equal square faces.
A cube.
Which unit would you use to measure volume: cm, cm2, or cm3
cm3
A cube has a volume of 27cm3. What is the side length?
3cm.
What formula is used to find the volume of a rectangular prism?
A = length x width x height
(A= l x w x h)
What shape are the faces of a cube?
Squares.
What 3D shape has a circular base and one vertex / apex? Draw it out.
A box has a volume of 24cm3. Write one possible set of dimensions.
Answers may vary (e.g., 2cm x 3cm x 4cm).
Which changes faster as a shape grows: surface area or volume?
Volume.
Find the volume using the following measurements.
Length = 4cm, Width = 3cm, Height = 2cm
V = l x w x h
V = 4cm x 3cm x 2cm
V= 24cm3
How many faces does a rectangular prism have? How many edges? How many vertices? Draw it out!
6 faces, 12 edges, 8 vertices.
What shape has 2 circular bases and one curved surface? Draw the net for it.
Cylinder.
Why do we use cm3 instead of cm when measuring volume?
Because volume measures 3D space (length x width x height).
True or False: Surface area and volume are the same thing. If not, explain the difference.
False.
Surface area measures the total area covering the outside of an object (2D measurement in square units), while volume measures the space inside an object, or how much it can hold (3D measurement in cubic units).
A box is 12cm long, 6cm wide, and 10cm high. What is the volume?
V = l x w x h
V = 12cm x 6cm x 10cm
V = 720cm3
Find the surface area of a cube with a side length of 2cm. Show your work & draw the net of a cube.
24cm2
How many vertices does a triangular prism have?
6.
A cube has a side length of 10cm. What is its volume in cm3?
1000cm3
A prism has a volume 60cm3 and base area 12cm2. What is the height.
5cm
If you double the height of a rectangular prism, what happens to the volume?
It doubles.
Why is surface area important in real life?
Which shape would hold more: a thin cylinder or a wide cylinder (same height)?
The wider one (larger base area = more volume)
Which is larger 1m3 or 1 000cm3?
1m3 (1m3 = 1 000 000cm3)
Explain why a larger box might not always have more surface area than a smaller one.
Shape and dimensions affect surface area differently than volume.