To solve these problems, we need to calculate the volume of different 3D shapes. The general rule for prisms (like boxes and cylinders) is:
Volume = Area of the Base × Length (or Height)
Let’s go through each question one by one.
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Question 1
(a) Rectangular Prism (Cuboid)
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Formula: Volume = Length × Width × Height
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Given: Length = 12 cm, Width = 2 cm, Height = 10 cm
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Calculation: $12 \times 2 \times 10 = 240$
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Answer: 240 cm³
(b) Cube
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Formula: Volume = Side × Side × Side
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Given: Side = 14 mm
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Calculation: $14 \times 14 \times 14$
* $14 \times 14 = 196$
* $196 \times 14 = 2744$
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Answer: 2744 mm³
(c) Triangular Prism
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Formula: Volume = (Area of Triangle) × Length
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Area of Triangle: $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 15 \times 4 = 30 \text{ mm}^2$
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Length of prism: 30 mm
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Calculation: $30 \times 30 = 900$
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Answer: 900 mm³
(d) Cylinder
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Formula: Volume = $\pi \times r^2 \times h$
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Given: Radius ($r$) = 5 cm, Height ($h$) = 10 cm, $\pi = 3.14$
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Calculation:
* $r^2 = 5 \times 5 = 25$
* $25 \times 10 = 250$
* $250 \times 3.14 = 785$
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Answer: 785 cm³
(e) Triangular Prism
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Formula: Volume = (Area of Triangle) × Length
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Area of Triangle: The triangle has a base of 12 m and a height of 16 m.
* $\text{Area} = \frac{1}{2} \times 12 \times 16 = 6 \times 16 = 96 \text{ m}^2$
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Length of prism: 30 m
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Calculation: $96 \times 30 = 2880$
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Answer: 2880 m³
(f) Cylinder
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Formula: Volume = $\pi \times r^2 \times h$
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Given: Diameter = 12 cm (so Radius $r = 6$ cm), Height ($h$) = 9 cm, $\pi = 3.14$
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Calculation:
* $r^2 = 6 \times 6 = 36$
* $36 \times 9 = 324$
* $324 \times 3.14 = 1017.36$
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Answer: 1017.36 cm³
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Question 2
(a) Volume of Fish Tank
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Shape: Rectangular Prism
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Formula: Length × Width × Height
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Given: 32 cm, 91 cm, 35 cm
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Calculation: $32 \times 91 \times 35$
* $32 \times 91 = 2912$
* $2912 \times 35 = 101920$
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Answer: 101920 cm³
(b) Convert to Litres
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Conversion: $1000 \text{ cm}^3 = 1 \text{ litre}$
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Calculation: $101920 \div 1000 = 101.92$
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Answer: 101.92 litres
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Question 3
(a) Name of the Solid
* The net has two triangular ends and three rectangular sides.
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Answer: Triangular Prism
(b) Volume of the Solid
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Formula: Volume = (Area of Triangle) × Length
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Area of Triangle: Base = 6 m, Height = 3 m
* $\text{Area} = \frac{1}{2} \times 6 \times 3 = 9 \text{ m}^2$
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Length of prism: 14 m
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Calculation: $9 \times 14 = 126$
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Answer: 126 m³
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Final Answer:
1. (a) 240 cm³, (b) 2744 mm³, (c) 900 mm³, (d) 785 cm³, (e) 2880 m³, (f) 1017.36 cm³
2. (a) 101920 cm³, (b) 101.92 litres
3. (a) Triangular Prism, (b) 126 m³
Parent Tip: Review the logic above to help your child master the concept of volume of prism and cylinders worksheet.
