SME
Grade 10 Math · Problem type
Mass of a ball from its density
Use this for “A steel ball has radius 1.5 cm and steel is 7.8 g/cm³. Find its mass.”
Diagram
V = 4/3 × π × r³
V
=
4
3
×
π
×
1.5
3
V = 4.5π ≈ 14.14 cm³
Density: 7.8 g/cm³
Mass: 110.27 g
This is an example. Type your own values to start a new problem.
V (cm³)
=
4
3
×
π
×
r
3
ρ (g/cm³)
=
m (g)
÷
V (cm³)
Formulas
V
=
4
×
π
×
r
3
3
14.14
=
4
×
π
×
1.5
3
3
ρ
=
m
V
7.8
=
110.27
14.14
Assumptions
•
Model the ball as a sphere: V = 4πr³ ÷ 3.
•
Mass is density times volume: m = ρV.
•
Given the mass and the material, work back to the volume first, then the radius.
Step-by-step
WE KNOW
r = 1.5 cm, ρ = 7.8 g/cm³
FIND
volume (V), mass (m)
Step 1 · Find volume (V)
Use V = 4 × π × r³ ÷ 3
The
volume
of
a
sphere
is
4π
r
3
3
.
V
=
4
×
π
×
1.5
3
3
V
=
4π
×
3.375
3
V
=
13.5π
3
V
=
14.137
cm³
Step 2 · Find mass (m)
Use ρ = m ÷ V
Each
cubic
centimeter
has
ρ
grams:
multiply.
m
=
ρ
×
V
m
=
7.8
×
14.137
m
=
110.27
g
Check
Put the numbers back in. Both sides should match.
14.137
≈
4
×
π
×
1.5
3
3
✓
7.8
≈
110.27
14.137
✓
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