Karina has 4 tanks on her tractor. Each tank is a cylinder with diameter 80 cm and height 160 cm. The tanks are to be filled completely with a mixture of fertiliser and water. The fertiliser has to be mixed with water in the ratio 1:100 by volume. Karina has 32 litres of fertiliser. 1 litre = 1000 cm³. Has Karina enough fertiliser for the 4 tanks? You must show how you get your answer.

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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 tanks are to be filled completely with a mixture of fertiliser... show full transcript

Worked Solution & Example Answer:Karina has 4 tanks on her tractor - Edexcel - GCSE Maths - Question 4 - 2022 - Paper 3

Step 1

Find the volume of 1 tank

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Answer

To calculate the volume of one tank, we use the formula for the volume of a cylinder:

$V = ext{base area} imes ext{height}$

The base area can be calculated using the formula:

$ext{base area} = rac{ ext{diameter}^2 imes ext{π}}{4}$

Given:

Diameter = 80 cm
Radius = \frac{80}{2} = 40 ext{ cm}
Height = 160 cm

Thus, the base area is:

$ext{base area} = rac{80^2 imes rac{22}{7}}{4} ext{ cm}^2 = 1600 imes rac{22}{7} ext{ cm}^2$

Calculating this gives:

$ext{base area} \approx 5026.67 ext{ cm}^2$

Now substituting into the volume formula:

$V = 5026.67 ext{ cm}^2 \times 160 ext{ cm} = 804267.04 ext{ cm}^3$

So the volume of one tank is approximately 804,267.04 cm³.

Step 2

Find the total volume for 4 tanks

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Answer

The total volume for 4 tanks is:

$ext{Total volume} = 4 \times 804267.04 ext{ cm}^3 \approx 3217068.16 ext{ cm}^3$

Step 3

Calculate the volume of fertiliser needed

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Answer

The total mixture ratio is 1 part fertiliser to 100 parts water, making a total of 101 parts.

Thus, the volume of fertiliser needed for 4 tanks can be calculated as:

$ext{Volume of fertiliser} = \frac{1}{101} \times ext{Total volume}$

Substituting in the total volume:

$ext{Volume of fertiliser} \approx \frac{1}{101} \times 3217068.16 \text{ cm}^3 \approx 31800.17 \text{ cm}^3$

Converting to litres, we have:

$\text{Volume of fertiliser (litres)} \approx \frac{31800.17}{1000} \approx 31.8 ext{ litres}$

Step 4

Determine if Karina has enough fertiliser

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Answer

Karina has 32 litres of fertiliser available, which is greater than the 31.8 litres required for the 4 tanks. Therefore, Karina has enough fertiliser for the tanks.

Karina has 4 tanks on her tractor - Edexcel - GCSE Maths - Question 4 - 2022 - Paper 3

Worked Solution & Example Answer:Karina has 4 tanks on her tractor - Edexcel - GCSE Maths - Question 4 - 2022 - Paper 3

Find the volume of 1 tank

Find the total volume for 4 tanks

Calculate the volume of fertiliser needed

Determine if Karina has enough fertiliser

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