SME
Grade 8 Math · Geometry
Volume of cylinders, cones and spheres
Use this for “A cylinder has a radius of 4 cm and a height of 9 cm. What is its volume?”
Diagram
V = π × r² × h
V = π × 5² × 8 = 200π ≈ 628.32 cm³
This is an example. Type your own values to start a new problem.
V
=
π
×
r
2
×
h
d
Diameter
calculated
B
Base area
worked out (not typed)
Formulas
d
=
2
×
r
(diameter
=
2
×
radius)
10 = 2 × 5
B
=
π
×
r
2
(base
area
=
π
×
radius²)
25π
=
π
×
5
2
V
=
B
×
h
(volume
=
base
area
×
height)
200π = 25π × 8
Assumptions
•
The base is a circle of radius r; its area is π × r².
•
A cylinder is that circle stacked h high: V = π × r² × h.
•
Doubling the height doubles the volume; doubling the radius makes it 4 times.
•
Round to the nearest cubic unit when the question asks: 200π ≈ 628.
Step-by-step
WE KNOW
r = 5 cm (radius), h = 8 cm (height)
FIND
diameter (d), base area (B), volume (V)
Step 1 · Find diameter (d)
Use d = 2 × r (diameter = 2 × radius)
The diameter is two radii.
d
=
2
×
5
d
=
10
cm
Step 2 · Find base area (B)
Use B = π × r² (base area = π × radius²)
The
base
is
a
circle:
π
×
r
2
.
B
=
π
×
5
2
B
=
25
×
π
B
=
25π
cm²
(≈
78.54
cm²)
Step 3 · Find volume (V)
Use V = B × h (volume = base area × height)
Stack
the
base
h
high.
V
=
25π
×
8
V
=
200π
cm³
(≈
628.32
cm³)
Check
Put the numbers back in. Both sides should match.
10 = 2 × 5 ✓
25π
=
π
×
5
2
✓
200π = 25π × 8 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
More problem types
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?”
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?”