SME
Grade 10 Math · Problem type
Volume of a pyramid
Use this for “A square pyramid has base side 6 cm and height 10 cm. Find its volume.”
Diagram
The cut is a square: 3 × 3 = 9 cm².
Cuts parallel to the base shrink toward the top.
V = 1/3 × 6 × 6 × 10 = 120 cm³
This is an example. Type your own values to start a new problem.
V (cm³)
=
1
3
×
b
2
×
h
Formulas
V
=
b
2
×
h
3
120
=
6
2
×
10
3
Assumptions
•
The base is a square with side b; h is the straight-up height to the tip.
•
A pyramid holds one third of the prism with the same base and height: V = ⅓b²h.
•
Level cuts are smaller squares, shrinking evenly to the tip.
Step-by-step
WE KNOW
b = 6 cm, h = 10 cm
FIND
volume (V)
Step 1 · Find volume (V)
Use V = b² × h ÷ 3
One third of the prism with the same base and height.
V
=
6
2
×
10
3
V
=
36
×
10
3
V
=
360
3
V
=
120
cm³
Check
Put the numbers back in. Both sides should match.
120
=
6
2
×
10
3
✓
Topic check
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