Volume of 3D Shapes Worksheets | Questions and Revision | MME - Free Printable

Let’s solve this step by step.

The shape is made of two parts:
- A cone on top
- A cylinder at the bottom

We need to find the total volume of the whole shape.

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Step 1: Find the radius

The diagram shows the diameter of the base is 4 mm.

So, radius = diameter ÷ 2 = 4 ÷ 2 = 2 mm

This radius is the same for both the cone and the cylinder.

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Step 2: Volume of the cone

Formula for volume of a cone:
> V_cone = (1/3) × π × r² × h

Here:
- r = 2 mm
- h = 5.5 mm (height of the cone part)

Plug in the numbers:

V_cone = (1/3) × π × (2)² × 5.5
= (1/3) × π × 4 × 5.5
= (1/3) × π × 22
≈ (1/3) × 3.1416 × 22
≈ (0.3333) × 69.1152
≈ 23.038 mm³

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Step 3: Volume of the cylinder

Formula for volume of a cylinder:
> V_cylinder = π × r² × h

Here:
- r = 2 mm
- h = 3 mm (height of the cylinder part)

Plug in the numbers:

V_cylinder = π × (2)² × 3
= π × 4 × 3
= π × 12
≈ 3.1416 × 12
≈ 37.699 mm³

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Step 4: Add them together

Total volume = V_cone + V_cylinder
≈ 23.038 + 37.699
≈ 60.737 mm³

Let’s round it to one decimal place as the measurements are given to one decimal:

→ 60.7 mm³

But let’s double-check our math with exact fractions to be sure.

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Double-check using exact values:

V_cone = (1/3) × π × 4 × 5.5 = (1/3) × π × 22 = (22/3)π

V_cylinder = π × 4 × 3 = 12π

Total = (22/3)π + 12π = (22/3 + 36/3)π = (58/3)π

Now calculate (58/3) × π:

58 ÷ 3 ≈ 19.3333
19.3333 × 3.1416 ≈ ?

Let’s compute:

19.3333 × 3 = 58
19.3333 × 0.1416 ≈ ?

First, 19.3333 × 0.1 = 1.93333
19.3333 × 0.04 = 0.773332
19.3333 × 0.0016 = 0.03093328

Add those:
1.93333 + 0.773332 = 2.706662
+ 0.03093328 ≈ 2.737595

So total ≈ 58 + 2.7376 = 60.7376 mm³

Same as before.

Rounded to one decimal: 60.7 mm³

But wait — sometimes problems expect you to use π = 3.14 exactly.

Let’s try that:

(58/3) × 3.14 = ?

58 × 3.14 = 182.12
Then divide by 3: 182.12 ÷ 3 = 60.7066... → still 60.7 mm³

Perfect.

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Final Answer:
60.7 mm³