In this lesson:
By the end of this lesson, you will be able to:
You already know how to find areas of 2D shapes:
Volume extends area into the third dimension — it is area times depth.
For any solid with a uniform cross-section — same shape through:
The base can be any shape — rectangle or circle.
A cylinder has radius 5 cm and height 12 cm.
Step 1: Identify and . Step 2: Substitute. Step 3: Simplify.
A box has length 3 cm, width 4 cm, height 5 cm.
What is its volume?
Think for a moment before the next slide…
Cones and pyramids taper to a point — they hold less than the corresponding prism or cylinder.
If it points, multiply by .
A cone has radius 6 in and height 10 in.
Key: The formula is the cylinder formula multiplied by .
A square pyramid: base edge 8 m, height 9 m.
Step 1: Square base →
Step 2: Apply :
Key: Identify the base shape first. Square → .
A sphere has no flat base or height — its volume depends only on radius.
A sphere has diameter 18 cm.
Step 1: cm ← Always find r first
Step 2:
Three identical cones fit inside one cylinder with the same base and height.
True or false?
Think before advancing…
For every SAT volume question:
A cylindrical tank holds cubic feet. The height is 20 feet. Find the radius.
Set up:
Solve:
A cylinder and a cone have the same base radius and height. The cylinder holds 240 cm³. How much does the cone hold?
Key insight: Same base and height → cone holds exactly one-third as much.
Try these problems on your own:
Pause and work through each before advancing.
1. Sphere, :
2. Prism, :
3. Cone, , :
Diameter given? Write first
Sphere volume uses , not
Next lesson: Effects of Scaling on Area and Volume
You will learn:
These scaling rules are SAT time-savers.