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AQA GCSE · Question 05.3 · Bonding structure and the properties of matter
Figure 6 represents a cubic nanoparticle with side length 3 nm. The volume of the cubic nanoparticle is 27 nm³. Calculate:\n• the surface area of the cubic nanoparticle\n• the simplest whole number ratio of surface area : volume for the cubic nanoparticle.\nUse the equation: surface area of cubic nanoparticle = 6 × surface area of one face
Figure 6 represents a cubic nanoparticle with side length 3 nm. The volume of the cubic nanoparticle is 27 nm³. Calculate:\n• the surface area of the cubic nanoparticle\n• the simplest whole number ratio of surface area : volume for the cubic nanoparticle.\nUse the equation: surface area of cubic nanoparticle = 6 × surface area of one face
How to approach this question
**Part 1: Surface Area**\n1. A cube has 6 identical square faces.\n2. Calculate the area of one square face: Area = side length × side length.\n3. Multiply the area of one face by 6 to get the total surface area.\n\n**Part 2: Surface Area to Volume Ratio**\n1. Write down the ratio using the surface area you just calculated and the volume given in the question (27 nm³).\n2. Simplify the ratio to its simplest whole number form by dividing both sides by their greatest common divisor.
Full Answer
**Surface Area:**\nArea of one face = length × width = 3 nm × 3 nm = 9 nm²\nTotal surface area = 6 × area of one face = 6 × 9 nm² = 54 nm²\n\n**Surface Area to Volume Ratio:**\nRatio = Surface Area : Volume\nRatio = 54 : 27\nTo simplify, divide both sides by the smallest number (27):\nRatio = (54/27) : (27/27)\nRatio = 2 : 1
**1. Calculate the surface area:**\nA cube has 6 square faces. The side length of the cube is 3 nm.\nThe area of one face is length × width = 3 nm × 3 nm = 9 nm².\nThe total surface area is 6 × (area of one face) = 6 × 9 nm² = 54 nm².\n\n**2. Calculate the surface area to volume ratio:**\nThe volume is given as 27 nm³.\nThe ratio of surface area to volume is 54 : 27.\nTo simplify this ratio, we find the greatest common divisor of 54 and 27, which is 27.\nDivide both sides of the ratio by 27:\n(54 ÷ 27) : (27 ÷ 27)\nThis simplifies to **2 : 1**.
Common mistakes
✗ Forgetting to multiply the area of one face by 6.\n✗ Calculating the volume instead of using the given value.\n✗ Not simplifying the ratio, or simplifying it incorrectly.
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