Surface Area of Cylinders online exercise for - Free Printable

Let’s solve each problem step by step.

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Problem 1: Use the net of the cylinder to calculate the following. (Use π = 3.14)

We are given:
- Radius of circle = 5 cm
- Height of rectangle (which is the height of the cylinder) = 11 cm

The net has:
- Two circles (top and bottom)
- One rectangle (the side when unrolled)

Step 1: Area of Top Circle

Formula for area of a circle:
A = π × r²
= 3.14 × 5²
= 3.14 × 25
= 78.5 cm²

Step 2: Area of Bottom Circle

Same as top circle → 78.5 cm²

Step 3: Area of Rectangle

When you unroll the side of a cylinder, the rectangle’s:
- Width = circumference of the circle = 2πr
- Height = height of cylinder = 11 cm

So, width = 2 × 3.14 × 5 = 31.4 cm
Area = width × height = 31.4 × 11 = 345.4 cm²

Step 4: Surface Area of Cylinder

Add all three parts:
Top + Bottom + Rectangle
= 78.5 + 78.5 + 345.4
= 157 + 345.4
= 502.4 cm²

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Problem 2(a): Calculate volume and surface area of cylinder with radius 3m, height 11m

Given:
- Radius r = 3 m
- Height h = 11 m
- π = 3.14

Volume Formula: V = π × r² × h
V = 3.14 × 3² × 11
= 3.14 × 9 × 11
= 28.26 × 11
= 310.86 m³

Surface Area Formula: SA = 2πr² + 2πrh
First part (two circles): 2 × 3.14 × 3² = 2 × 3.14 × 9 = 56.52
Second part (rectangle): 2 × 3.14 × 3 × 11 = 6.28 × 33 = 207.24
Total SA = 56.52 + 207.24 = 263.76 m²

Wait — but the question only asks for VOLUME in part (a). Let me check again.

Looking back at the worksheet:

> 2. Calculate the volume and surface area of the following cylinders.
> (a) [cylinder with 3m radius, 11m height] → asks for VOLUME = ___ m³
> (b) [cylinder with diameter 14ft, height 5ft] → asks for SURFACE AREA = ___ ft²

So for (a), we only need volume → 310.86 m³

For (b):

Given:
- Diameter = 14 ft → so radius = 7 ft
- Height = 5 ft
- π = 3.14

Surface Area = 2πr² + 2πrh
= 2×3.14×7² + 2×3.14×7×5
= 2×3.14×49 + 2×3.14×35
= 6.28×49 + 6.28×35
= 307.72 + 219.8
= 527.52 ft²

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Problem 3: Sam has a cylindrical fish tank with an open top. Height 30cm, radius 20cm. What is total surface area? (Use π = 3.14)

Open top means: no top circle. So we have:
- Bottom circle (area = πr²)
- Side rectangle (area = 2πrh)

No top circle!

So:

Bottom area = 3.14 × 20² = 3.14 × 400 = 1256 cm²

Side area = 2 × 3.14 × 20 × 30
= 6.28 × 600
= 3768 cm²

Total surface area = 1256 + 3768 = 5024 cm²

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Final Answer:

1.
Area of Top Circle: 78.5 cm²
Area of Bottom Circle: 78.5 cm²
Area of Rectangle: 345.4 cm²
Surface Area of Cylinder: 502.4 cm²

2.
(a) VOLUME = 310.86 m³
(b) SURFACE AREA = 527.52 ft²

3.
SURFACE AREA = 5024 cm²