Liquid A and liquid B are mixed together in the ratio 2:13 by volume to make liquid C. Liquid A has density 1.21 g/cm³ Liquid B has density 1.02 g/cm³ A cylindrical container is filled completely with liquid C. The cylinder has radius 3 cm and height 25 cm. Work out the mass of the liquid in the container. Give your answer correct to 3 significant figures. You must show all your working.

GCSE Edexcel Maths Ratio Analysis and Problem Solving: Liquid A and liquid B are mixed

Liquid A and liquid B are mixed together in the ratio 2:13 by volume to make liquid C - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 3

Question 14

Liquid A and liquid B are mixed together in the ratio 2:13 by volume to make liquid C. Liquid A has density 1.21 g/cm³ Liquid B has density 1.02 g/cm³ A cylindrica... show full transcript

Worked Solution & Example Answer:Liquid A and liquid B are mixed together in the ratio 2:13 by volume to make liquid C - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 3

Step 1

Step 1: Find the volume of liquid C

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Answer

The total volume of the cylinder can be calculated using the formula for the volume of a cylinder:

$V = ext{radius}^2 imes ext{height} imes ext{π}$

Given that the radius is 3 cm and the height is 25 cm, we can substitute these values into the formula:

$V = (3^2) imes 25 imes ext{π}$ $V = 9 imes 25 imes 3.14159 \approx 706.5 ext{ cm}^3$

Step 2

Step 2: Find the volumes of liquid A and B in liquid C

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Answer

Given the mixing ratio of liquid A to liquid B is 2:13, the total parts of the mixture is:

$2 + 13 = 15$

Next, we can find the volume of liquid A and liquid B within the total volume of liquid C:

Volume of liquid A:

$V_A = rac{2}{15} imes 706.5 \approx 94.2 ext{ cm}^3$

Volume of liquid B:

$V_B = rac{13}{15} imes 706.5 \approx 612.3 ext{ cm}^3$

Step 3

Step 3: Calculate the mass of liquids A and B

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Answer

To find the mass of each liquid, we use the formula:

$ext{mass} = ext{density} imes ext{volume}$

Mass of liquid A:

$M_A = 1.21 ext{ g/cm}^3 imes 94.2 ext{ cm}^3 \approx 113.92 ext{ g}$

Mass of liquid B:

$M_B = 1.02 ext{ g/cm}^3 imes 612.3 ext{ cm}^3 \approx 624.65 ext{ g}$

Step 4

Step 4: Find the total mass of liquid C

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Answer

Now we sum the masses of liquid A and B to get the total mass of liquid C:

$ext{Total Mass} = M_A + M_B \approx 113.92 + 624.65 \approx 738.57 ext{ g}$

Rounding to 3 significant figures, the final answer is:

738 g.

Liquid A and liquid B are mixed together in the ratio 2:13 by volume to make liquid C - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 3

Worked Solution & Example Answer:Liquid A and liquid B are mixed together in the ratio 2:13 by volume to make liquid C - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 3

Step 1: Find the volume of liquid C

Step 2: Find the volumes of liquid A and B in liquid C

Step 3: Calculate the mass of liquids A and B

Step 4: Find the total mass of liquid C

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