SME
Grade 8 Math · Problem type
Volume of a cone
Use this for “A cone has radius 3 and height 7. What is its volume?” or “A cone holds 18π with height 6: its radius?”
Diagram
V = 1/3 × π × r² × h
V = 1/3 × π × 6² × 8
= 96π ≈ 301.59 cm³
Its water fills 1/3 of the cylinder 8 cm tall: 288π × 1/3 = 96π
This is an example. Type your own values to start a new problem.
V
=
1
3
×
π
×
r
2
×
h
Formulas
V
=
1
3
×
π
×
r
2
×
h
(volume
=
1/3
×
π
×
radius²
×
height)
96π
=
1
3
×
π
×
6
2
×
8
Assumptions
•
The cone and the cylinder have the same radius and height.
•
Three cones of water fill the cylinder, so a cone holds 1/3 of it.
•
V = 1/3 × π × r² × h.
Step-by-step
WE KNOW
r = 6 cm (radius), h = 8 cm (height)
FIND
volume (V)
Step 1 · Find volume (V)
Use V = 1/3 × π × r² × h (volume = 1/3 × π × radius² × height)
A third of the cylinder with the same base and height.
V
=
1
3
×
π
×
6
2
×
8
V
=
1
3
×
36
×
8
×
π
V
=
12
×
8
×
π
V
=
96
×
π
V
=
96π
cm³
(≈
301.59
cm³)
Check
Put the numbers back in. Both sides should match.
96π
=
1
3
×
π
×
6
2
×
8
✓
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Related lessons
Volume of cylinders, cones and spheres
Main lesson
Volume of a sphere
Use this for “A ball of radius 3 cm: its volume” or “A ball just fits in a 4-inch box: is its volume more or less than half of 4³?”
Change one dimension
Use this for “A cylinder holds 60π cm³. What does it hold at 3 times the height?” or “Quadruple the radius of a cone.”
Which volume formula?
Use this for “Which formula finds the volume of a funnel?”