GCSE exam questions on volume calculations from various past papers.

I'll solve each problem step by step, checking my calculations carefully.

Question 1: Orange Juice Glasses

Given:
- Carton contains 4 litres of orange juice
- Cylindrical glasses: height = 10 cm, radius = 3 cm

Step 1: Convert litres to cubic centimeters
4 litres = 4 × 1000 = 4000 cm³

Step 2: Calculate volume of one glass
Volume of cylinder = π × r² × h
= π × 3² × 10
= π × 9 × 10
= 90π cm³
≈ 282.74 cm³ (using π ≈ 3.14159)

Step 3: Calculate number of glasses
Number of glasses = Total volume ÷ Volume per glass
= 4000 ÷ 282.74
≈ 14.15

Since we can only fill complete glasses, the answer is 14 glasses.

Let me verify: 14 × 282.74 = 3958.36 cm³ (which is less than 4000 cm³ ✓)

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Question 2: Cuboid Boxes

Given:
- Larger box: 20cm × 10cm × 20cm
- Smaller boxes: 5cm × 5cm × 2cm
- Already filled with 70 smaller boxes

Step 1: Calculate volume of larger box
Volume = 20 × 10 × 20 = 4000 cm³

Step 2: Calculate volume of one smaller box
Volume = 5 × 5 × 2 = 50 cm³

Step 3: Calculate total capacity in terms of smaller boxes
Total boxes that can fit = 4000 50 = 80 boxes

Step 4: Calculate how many more can be added
More boxes = 80 - 70 = 10 boxes

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Question 3: Cylinder

Given:
- Radius = 5 cm
- Part (a): Find circumference
- Part (b): Volume = 250 cm³, find height

Part (a): Circumference of circular end
Circumference = 2πr
= 2 × π × 5
= 10π cm
≈ 31.42 cm

Part (b): Height of cylinder
Volume = π × r² × h
250 = π × 5² × h
250 = π × 25 × h
250 = 25πh
h = 250 (25π)
h = 10 ÷ π
h ≈ 3.18 cm

Let me verify: π × 5² × 3.18 = π × 25 × 3.18 ≈ 250 cm³ ✓

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Question 4: Water Container

Given:
- Cuboid container: base 20cm × 20cm
- Initial water depth = 15 cm
- Tony adds 1000 cm³ of water
- Find new depth d

Step 1: Calculate initial volume of water
Initial volume = 20 × 20 × 15 = 6000 cm³

Step 2: Calculate new volume after adding water
New volume = 6000 + 1000 = 7000 cm³

Step 3: Calculate new depth
Volume = length × width × depth
7000 = 20 × 20 × d
7000 = 400d
d = 7000 ÷ 400
d = 17.5 cm

Let me verify: 20 × 20 × 17.5 = 7000 cm³ ✓

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Question 5: School Hall

Given:
- Cuboid hall: 30m long × 12m wide × 4m tall

Part (a): Volume of the hall
Volume = length × width × height
= 30 × 12 × 4
= 1440 m³

Part (b): Total area of the four walls

The four walls consist of:
- Two walls: 30m × 4m each
- Two walls: 12m × 4m each

Area of two longer walls = 2 × (30 × 4) = 2 × 120 = 240 m²
Area of two shorter walls = 2 × (12 × 4) = 2 × 48 = 96 m²

Total wall area = 240 + 96 = 336 m²

Alternatively: Perimeter × height = 2(30 + 12) × 4 = 2(42) × 4 = 84 × 4 = 336 m² ✓

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Final Answer:

Question 1: 14 glasses

Question 2: 10 more smaller boxes

Question 3:
(a) 31.4 cm (or 10π cm)
(b) 3.18 cm (or 10/π cm)

Question 4: 17.5 cm

Question 5:
(a) 1440 m³
(b) 336 m²