SME
Grade 10 Math · Problem type
Volume of a cone
Use this for “A cone has radius 3 cm and height 4 cm. Find its volume.”
Diagram
V = 1/3 × π × r² × h
V
=
1
3
×
π
×
3
2
×
4
V = 12π ≈ 37.7 cm³
This is an example. Type your own values to start a new problem.
V (cm³)
=
1
3
×
π
×
r
2
×
h
Formulas
V
=
π
×
r
2
×
h
3
12π
=
π
×
3
2
×
4
3
Assumptions
•
A cone holds one third of the cylinder with the same base and height.
•
So V = ⅓πr²h, with h the straight-up height, not the slant.
Step-by-step
WE KNOW
r = 3 cm, h = 4 cm
FIND
volume (V)
Step 1 · Find volume (V)
Use V = π × r² × h ÷ 3
One third of the cylinder with the same base and height.
V
=
π
×
3
2
×
4
3
V
=
π
×
9
×
4
3
V
=
9π
×
4
3
V
=
36π
3
V
=
12π
cm³
(≈
37.7
cm³)
Check
Put the numbers back in. Both sides should match.
12π
=
π
×
3
2
×
4
3
✓
Topic check
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