SME
Grade 8 Math · Problem type
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?”
Diagram
V = 4/3 × π × r³
V = 4/3 × π × 3³ = 36π ≈ 113.1 cm³
Its water fills 2/3 of the cylinder 6 cm tall: 54π × 2/3 = 36π
This is an example. Type your own values to start a new problem.
V
=
4
3
×
π
×
r
3
d
Diameter
calculated
C
Cube that just holds it
worked out (not typed)
Formulas
d
=
2
×
r
(diameter
=
2
×
radius)
6 = 2 × 3
V
=
4
3
×
π
×
r
3
(volume
=
4/3
×
π
×
radius³)
36π
=
4
3
×
π
×
3
3
C
=
d
3
(cube
that
just
holds
it
=
diameter³)
216
=
6
3
Assumptions
•
The sphere just fits in a cylinder: the same radius, and 2r tall.
•
Its water fills 2/3 of that cylinder, so V = 4/3 × π × r³.
•
The cube around it has edge 2r; the sphere is a little more than half of it.
Step-by-step
WE KNOW
r = 3 cm (radius)
FIND
diameter (d), volume (V), cube that just holds it (C)
Step 1 · Find diameter (d)
Use d = 2 × r (diameter = 2 × radius)
The diameter is two radii.
d
=
2
×
3
d
=
6
cm
Step 2 · Find volume (V)
Use V = 4/3 × π × r³ (volume = 4/3 × π × radius³)
Cube
the
radius,
then
multiply
by
4
3
and
by
π.
V
=
4
3
×
π
×
3
3
V
=
4
3
×
27
×
π
V
=
36
×
π
V
=
36π
cm³
(≈
113.1
cm³)
Step 3 · Find cube that just holds it (C)
Use C = d³ (cube that just holds it = diameter³)
The cube around the ball: its edge is the diameter.
C
=
6
3
C
=
216
cm³
Check
Put the numbers back in. Both sides should match.
6 = 2 × 3 ✓
36π
=
4
3
×
π
×
3
3
✓
216
=
6
3
✓
Topic check
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Related lessons
Volume of cylinders, cones and spheres
Main lesson
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?”
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?”