This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here's the solution to the problem. The problem describes a cuboid M and a cube N. a) Calculate the volume of cuboid M. b) The side length of cube N is equal to the height of cuboid M. Calculate the volume of cube N. c) There is a cube S, whose side length is 20% longer than the side length of cube N. i) Calculate the side length of cube S. ii) Calculate the difference in volume between cube N and cube S. a) Calculate the volume of cuboid M. Step 1: Identify the dimensions of cuboid M. From the image, the length of cuboid M is 8 cm, and the width is 5 cm. The area of one shaded face is given as 40 cm^2. This shaded face has dimensions 8 cm × height. So, 8 cm × height = 40 cm^2. Step 2: Calculate the height of cuboid M. Height = 40 cm^28 cm = 5 cm Step 3: Calculate the volume of cuboid M. The volume of a cuboid is given by length × width × height. Volume of M = 8 cm × 5 cm × 5 cm = 200 cm^3 The volume of cuboid M is 200 cm^3. b) The side length of cube N is equal to the height of cuboid M. Calculate the volume of cube N. Step 1: Determine the side length of cube N. The height of cuboid M is 5 cm (from part a). So, the side length of cube N is 5 cm. Step 2: Calculate the volume of cube N. The volume of a cube is given by side length^3. Volume of N = (5 cm)^3 = 5 cm × 5 cm × 5 cm = 125 cm^3 The volume of cube N is 125 cm^3. c) There is a cube S, whose side length is 20% longer than the side length of cube N. i) Calculate the side length of cube S. Step 1: Determine the side length of cube N. From part b), the side length of cube N is 5 cm. Step 2: Calculate the side length of cube S. The side length of cube S is 20% longer than the side length of cube N. Side length of S = Side length of N × (1 + 20\%) Side length of S = 5 cm × (1 + 0.20) Side length of S = 5 cm × 1.20 = 6 cm The side length of cube S is 6 cm. ii) Calculate the difference in volume between cube N and cube S. Step 1: Calculate the volume of cube S. The side length of cube S is 6 cm (from part c.i). Volume of S = (6 cm)^3 = 6 cm × 6 cm × 6 cm = 216 cm^3 Step 2: Calculate the difference in volume between cube N and cube S. The volume of cube N is 125 cm^3 (from part b). Difference in volume = Volume of S - Volume of N Difference in volume = 216 cm^3 - 125 cm^3 = 91 cm^3 The difference in volume between cube N and cube S is 91 cm^3. Drop the next question!