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Karina has 4 tanks on her tractor - Edexcel - GCSE Maths - Question 4 - 2022 - Paper 3
Question 4
Karina has 4 tanks on her tractor. Each tank is a cylinder with diameter 80 cm and height 160 cm. The 4 tanks are to be filled completely with a mixture of fertilis... show full transcript
Worked Solution & Example Answer:Karina has 4 tanks on her tractor - Edexcel - GCSE Maths - Question 4 - 2022 - Paper 3
Step 1
Calculate the volume of one tank
Answer
To determine the volume of one tank, we will use the formula for the volume of a cylinder:
The base area for a cylinder is given by:
ext{Base Area} = rac{1}{4} imes ext{Diameter}^2 imes rac{ ext{ ext{π}}}{4}
Substituting values:
- Diameter = 80 cm
- Height = 160 cm
- V = rac{1}{4} imes (80)^2 imes 160
- V = rac{1}{4} imes 6400 imes 160
Now, since there are 4 tanks, the total volume will be:
Step 2
Determine the amount of fertiliser needed
Answer
Given the ratio of fertiliser to water is 1:100, the total parts of the mixture is 1 + 100 = 101 parts. Thus, for the mixture:
- Fertiliser = 1 part
- Water = 100 parts
For every litre of fertiliser, there are 100 litres of water. So, we can express the amount of fertiliser needed for the total volume of tanks.
Let V be the total volume needed. Since 1 litre = 1000 cm³:
The volume of one part (fertiliser): ext{Volume of fertiliser} = rac{V_{total}}{101}
- Using the total volume, we find: ext{Volume of fertiliser} = rac{4096000}{101} \ ext{cm}^3
Step 3
Check if Karina has enough fertiliser
Answer
Karina has 32 litres of fertiliser:
- In cm³, this is:
Now, we compare this with the required amount:
- Required fertiliser = 40537.62 cm³
- Available fertiliser = 32000 cm³
Since 32000 cm³ is less than the required 40537.62 cm³, Karina does not have enough fertiliser for the 4 tanks.