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Volume and surface area

Volume and surface area for Access to HE Politics: what it means, how to set the working out, and the questions it is asked in.
  • Access to HE
  • Politics
  • Spec S3 · S14 · S10
  • 11 min read
  • 10 revision boxes

Introduction

2 boxes
4 min read

What is volume and surface area?

Listen to this box

Transcript

A short spoken summary of volume and surface area and where it is used.

A spoken walk-through of volume and surface area before you read the notes.
The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: ×10\times 10 moves every digit one column left.
2 rows

The volume and surface area reference table

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: ≈160\approx 160.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 1 column 4
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 2 column 4
Row 3 column 1
Row 3 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 3 column 4
Row 4 column 1
Row 4 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 4 column 4

Learning

6 boxes
5 steps

How to work with volume and surface area

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: 49=7\sqrt{49} = 7.
  1. Read the question and write down what is being asked for.
  2. Set out the working for volume and surface area in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 49=7\sqrt{49} = 7.
Answer: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Volume and surface area

Practise the routine version until it is automatic, then move to the multi-step questions.

  • Rule 1

    How volume and surface area behaves in the 1st of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 2

    How volume and surface area behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How volume and surface area behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
3 steps

How to work with volume and surface area

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: ×10\times 10 moves every digit one column left.
  1. Read the question and write down what is being asked for.
  2. Set out the working for volume and surface area in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ≈160\approx 160.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Volume and surface area

This idea appears again in the higher-mark questions, so it is worth over-learning.
The layout below is the one the mark scheme expects.

Diagram showing volume and surface area laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.

  • Rule 1

    How volume and surface area behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

    How volume and surface area behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7
3 steps

How to work with volume and surface area

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing volume and surface area laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: ×10\times 10 moves every digit one column left.
  1. Read the question and write down what is being asked for.
  2. Set out the working for volume and surface area in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 49=7\sqrt{49} = 7.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
2 rules

Key facts: Volume and surface area

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

  • Rule 1

    How volume and surface area behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

    How volume and surface area behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 3

    How volume and surface area behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

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Examples

2 boxes
4 marks · worked

Worked example: volume and surface area

Read the units in the question before you start; a converted unit is the most common slip.
The layout below is the one the mark scheme expects.

Diagram showing volume and surface area laid out step by step

The same idea drawn out, so the method is visible.
2 marks · worked

Practice question 10: 34×25\frac{3}{4} \times \frac{2}{5}

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: ×10\times 10 moves every digit one column left.

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Common questions

How many marks is volume and surface area usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the Access to HE Politics paper?
Yes — it sits in the Change over time strand.