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 Direct & Inverse Proportion: 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 13 - 2019 - Paper 3

Question 13

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 13 - 2019 - Paper 3

Step 1

Calculate the Volume of the Cylinder

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Answer

To find the volume (V) of the cylindrical container, we use the formula for the volume of a cylinder:

$V = ext{Base Area} imes ext{Height}$

The base area (A) of the cylinder is given by:

$A = ext{Radius}^2 imes ext{π} = (3 ext{ cm})^2 imes ext{π} = 9 ext{π} ext{ cm}^2$

Thus, the total volume is:

$V = 9 ext{π} ext{ cm}^2 imes 25 ext{ cm} = 225 ext{π} ext{ cm}^3 \ \\ ext{(Using } ext{π} ext{ ≈ 3.14:)} \\ V ≈ 706.86 ext{ cm}^3$

Step 2

Determine the Volumes of Liquids A and B

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Answer

Given the mixing ratio of liquid A to liquid B as 2:13,

Let the volumes of liquid A and B be represented as:

$ext{Volume of A (V_A)} = \frac{2}{15} V_C$ $ext{Volume of B (V_B)} = \frac{13}{15} V_C$

Substituting the volume of liquid C,

$V_A = \frac{2}{15} imes 706.86 ext{ cm}^3 ≈ 94.248 ext{ cm}^3$ $V_B = \frac{13}{15} imes 706.86 ext{ cm}^3 ≈ 612.612 ext{ cm}^3$

Step 3

Calculate the Masses of Liquids A and B

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Answer

Using the densities provided:

Mass of liquid A (M_A): $M_A = V_A imes ext{Density of A} = 94.248 ext{ cm}^3 imes 1.21 ext{ g/cm}^3 ≈ 113.922 ext{ g}$
Mass of liquid B (M_B): $M_B = V_B imes ext{Density of B} = 612.612 ext{ cm}^3 imes 1.02 ext{ g/cm}^3 ≈ 624.656 ext{ g}$

Step 4

Total Mass of the Liquid in the Container

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Answer

To find the total mass (M_T) of the liquid in the container:

$M_T = M_A + M_B ≈ 113.922 ext{ g} + 624.656 ext{ g} ≈ 738.578 ext{ g}$

Thus, the final mass of the liquid in the container, correct to 3 significant figures, is:

$M_T ≈ 739 ext{ g}$

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

Calculate the Volume of the Cylinder

Determine the Volumes of Liquids A and B

Calculate the Masses of Liquids A and B

Total Mass of the Liquid in the Container

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