Volume of Prisms and Cylinders worksheet with problems on calculating volumes of various 3D shapes, including prisms, cylinders, and a fish tank, using given dimensions and π = 3.14.

Let’s solve each problem step by step.

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1. Calculate the volume of the following shapes using π = 3.14, where necessary:

(a) Rectangular prism (box)
Dimensions: length = 12 cm, width = 2 cm, height = 10 cm
Volume = length × width × height
= 12 × 2 × 10
= 24 × 10
= 240 cm³

(b) Cube
All sides are equal. Side = 14 mm
Volume = side × side × side = 14³
= 14 × 14 × 14
First: 14 × 14 = 196
Then: 196 × 14
Break it down: 196 × 10 = 1960; 196 × 4 = 784 → 1960 + 784 = 2744 mm³

(c) Triangular prism
Base of triangle = 15 mm, height of triangle = 4 mm, length of prism = 30 mm
Area of triangular base = (base × height) ÷ 2 = (15 × 4) ÷ 2 = 60 ÷ 2 = 30 mm²
Volume = area of base × length = 30 × 30 = 900 mm³

(d) Cylinder
Radius = 5 cm, height = 10 cm
Volume = π × r² × h = 3.14 × 5² × 10
5² = 25
3.14 × 25 = 78.5
78.5 × 10 = 785 cm³

(e) Triangular prism (right triangle base)
Base of triangle = 12 m, height of triangle = 16 m, length of prism = 30 m
Area of triangular base = (12 × 16) ÷ 2 = 192 ÷ 2 = 96 m²
Volume = 96 × 30 = 2880 m³

Wait — let me double-check that multiplication:
96 × 30 = 96 × 3 × 10 = 288 × 10 = 2880 m³ ✔

(f) Cylinder
Diameter = 12 cm → radius = 6 cm, height = 9 cm
Volume = π × r² × h = 3.14 × 6² × 9
6² = 36
3.14 × 36 = let’s calculate:
3 × 36 = 108, 0.14 × 36 = 5.04 → total = 113.04
Now multiply by 9: 113.04 × 9
100 × 9 = 900
13 × 9 = 117
0.04 × 9 = 0.36
Total = 900 + 117 = 1017 + 0.36 = 1017.36 cm³

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2. Billy buys a fish tank. Dimensions: 32 cm by 91 cm by 35 cm.

(a) Volume in cm³
Volume = length × width × height = 32 × 91 × 35
Let’s do step by step:
First, 32 × 91
30 × 91 = 2730
2 × 91 = 182
Total = 2730 + 182 = 2912
Now, 2912 × 35
Break into: 2912 × 30 + 2912 × 5
2912 × 30 = 87,360
2912 × 5 = 14,560
Add them: 87,360 + 14,560 = 101,920 cm³

(b) Convert to litres
1000 cm³ = 1 litre
So, 101,920 ÷ 1000 = 101.92 litres

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3. Net of a shape

The net has two triangles and three rectangles → this is a triangular prism.

Looking at the net:
- The triangles have base = 6 m, height = 3 m (from dashed line)
- The rectangles connect them — one rectangle is 14 m long (this is the length of the prism)

(a) Name of solid: Triangular prism

(b) Volume
Area of triangular base = (base × height) ÷ 2 = (6 × 3) ÷ 2 = 18 ÷ 2 = 9 m²
Length of prism = 14 m
Volume = area of base × length = 9 × 14 = 126 m³

Double-check: 9 × 14 = 9×10 + 9×4 = 90 + 36 = 126 ✔

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Final Answer:

1.
(a) 240
(b) 2744
(c) 900
(d) 785
(e) 2880
(f) 1017.36

2.
(a) 101920
(b) 101.92

3.
(a) Triangular prism
(b) 126