Karina has 4 tanks on her tractor. Each tank is a cylinder with diameter 80cm and height 160cm. 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 = 1000cm³. Has Karina enough fertiliser for the 4 tanks? You must show how you get your answer.

GCSE Edexcel Maths Ratio Analysis and Problem Solving: Karina has 4 tanks on her tracto

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 80cm and height 160cm. The tanks are to be filled completely with a mixture of fertiliser a... 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 one tank

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Answer

To find the volume of a cylinder, we use the formula:

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

First, calculate the radius of the tank:

Diameter = 80cm, so the radius, r = 40cm.

The base area (A) is given by:

$A = rac{22}{7} r^2 = rac{22}{7} (40)^2 = rac{22}{7} imes 1600 = 5057.14 ext{ cm}^2$

Now, use the height (160cm) to find the volume of one tank:

$V = 5057.14 imes 160 = 809142.86 ext{ cm}^3$

Step 2

Calculate the total volume for 4 tanks

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Answer

Now, since there are 4 tanks, the total volume (V_total) is:

$V_{total} = 4 imes 809142.86 = 3232571.43 ext{ cm}^3$

Step 3

Determine the volume of fertiliser needed

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Answer

Given the ratio of fertiliser to water is 1:100, the total volume of mixture is:

$V_{mix} = 1 + 100 = 101$

The volume of fertiliser (V_fertiliser) needed can be calculated as:

$V_{fertiliser} = rac{V_{total}}{101} = rac{3232571.43}{101} = 31936.96 ext{ cm}^3$

Step 4

Convert fertiliser to litres and compare to available amount

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Answer

Convert cubic centimetres to litres:

$V_{fertiliser} = rac{31936.96}{1000} = 31.94 ext{ litres}$

Karina has 32 litres of fertiliser available. Since 31.94 litres < 32 litres, Karina has enough fertiliser for the 4 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 one tank

Calculate the total volume for 4 tanks

Determine the volume of fertiliser needed

Convert fertiliser to litres and compare to available amount

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