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.
ScanSolve AI Answer
You're on a roll — here are the solutions to the problems from the image: Part 1: Complete the table The formula for the volume of a cuboid is V = length × width × height. Row 1: Given: Length = 6 m, Width = 5 m, Height = 2 m Step 1: Calculate the volume. V = 6 m × 5 m × 2 m V = 60 m^3 Missing value: 60 m^3 Row 2: Given: Length = 7 m, Width = 6 m, Volume = 270 m^3 Step 1: Rearrange the volume formula to find height. Height = VolumeLength × Width Step 2: Substitute the values and calculate. Height = 270 m^37 m × 6 m Height = 270 m^342 m^2 Height = (45)/(7) m ≈ 6.43 m Missing value: (45)/(7) m or 6.43 m (approximately) Row 3: Given: Width = 50 cm, Height = 80 cm, Volume = 85000 cm^3 Step 1: Rearrange the volume formula to find length. Length = VolumeWidth × Height Step 2: Substitute the values and calculate. Length = 85000 cm^350 cm × 80 cm Length = 85000 cm^34000 cm^2 Length = (85)/(4) cm = 21.25 cm Missing value: 21.25 cm Row 4: Given: Length = 70 cm, Width = 50 cm, Height = 80 cm Step 1: Calculate the volume. V = 70 cm × 50 cm × 80 cm V = 280000 cm^3 Missing value: 280000 cm^3 Part 2: Word Problem The problem states: "The volume of the cuboid is 720000 cm³. If its base area is 2000 cm², what is its length?" Step 1: Recall the formula for the volume of a cuboid using base area. Volume = Base Area × Height In this context, "length" is likely referring to the missing dimension, which is the height of the cuboid, given the base area. Step 2: Substitute the given values into the formula. 720000 cm^3 = 2000 cm^2 × Height Step 3: Solve for the height (which the question refers to as "length"). Height = 720000 cm^32000 cm^2 Height = 360 cm The "length" (height) of the cuboid is 360 cm. What's next?