SME
Grade 10 Math · Problem type
Surface area of a cylinder
Use this for “Find the surface area of a can with radius 4 cm and height 7 cm.”
Diagram
Net
Solid
The net: two circles and a rectangle as long as the circumference, 2πr.
S
=
2
×
π
×
4
2
+
2π
×
4
×
7
S = 88π ≈ 276.46 cm²
This is an example. Type your own values to start a new problem.
S (cm²)
=
2π
×
r
2
+
2π
×
r
×
h
Formulas
S
=
2
×
π
×
r
2
+
2
×
π
×
r
×
h
88π
=
2
×
π
×
4
2
+
2
×
π
×
4
×
7
Assumptions
•
Unrolled, a cylinder is two circles and a rectangle.
•
The rectangle wraps the circle: it is as long as the circumference 2πr and as tall as h.
•
So S = 2πr² + 2πrh.
Step-by-step
WE KNOW
r = 4 cm, h = 7 cm
FIND
surface area (S)
Step 1 · Find surface area (S)
Use S = 2 × π × r² + 2 × π × r × h
Two
circles
and
a
rectangle
2πr
long
and
h
tall.
S
=
2
×
π
×
4
2
+
2
×
π
×
4
×
7
S
=
2
×
16
×
π
+
2
×
4
×
7
×
π
S
=
32
×
π
+
8
×
7
×
π
S
=
32π
+
56
×
π
S
=
32π
+
56π
S
=
88π
cm²
(≈
276.46
cm²)
Check
Put the numbers back in. Both sides should match.
88π
=
2
×
π
×
4
2
+
2
×
π
×
4
×
7
✓
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