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AQA GCSE · Question 23.2 · Geometry and Measures
The prism has
volume = 3500 cm³
and
length = 20 cm
Work out the area of the cross-section of the prism.
The prism has
volume = 3500 cm³
and
length = 20 cm
Work out the area of the cross-section of the prism.
How to approach this question
1. **Recall the formula for the volume of a prism:**
Volume = Area of cross-section × length.
2. **Rearrange the formula to find the area of the cross-section:**
Area of cross-section = Volume ÷ length.
3. **Substitute the given values into the formula:**
Area of cross-section = 3500 cm³ ÷ 20 cm.
4. **Calculate the result:**
3500 ÷ 20 = 350 ÷ 2 = 175.
5. **Include the units:** The area is 175 cm².
Full Answer
The volume of any prism is calculated using the formula:
Volume = Area of cross-section × Length
In this question, we are given the volume and the length, and we need to find the area of the cross-section. The cross-section is the shape of the hexagonal end face.
We can rearrange the formula to make the area of the cross-section the subject:
Area of cross-section = Volume / Length
Now, we substitute the values we are given:
- Volume = 3500 cm³
- Length = 20 cm
Area of cross-section = 3500 / 20
To calculate this without a calculator, we can simplify the fraction by dividing both the top and bottom by 10:
Area = 350 / 2
Now, we just need to halve 350:
Area = 175
The units for area will be cm². So the answer is 175 cm².
Common mistakes
✗ Multiplying the volume and length instead of dividing.\n✗ Making an error in the division calculation.
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