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
Here are the calculations for the cubic units (volume) and square areas (surface area) for each problem. Problem 1: Calculate the cubic units. Count the cube units (from the top image of the prism): The prism has dimensions: Length = 5 units, Width = 4 units, Height = 3 units. Volume: V = Length × Width × Height V = 5 units × 4 units × 3 units V = 60 cubic units Surface Area: SA = 2(Length × Width + Length × Height + Width × Height) SA = 2(5 × 4 + 5 × 3 + 4 × 3) SA = 2(20 + 15 + 12) SA = 2(47) SA = 94 square units Write it down. For "4 cubic units x 5 cubic units x 3 cubic units": V = 4 units × 5 units × 3 units V = 60 cubic units For "2 x (5 x 4) + 2 x (3 x 4) + 2 x (5 x 3)": SA = 2(20) + 2(12) + 2(15) SA = 40 + 24 + 30 SA = 94 square units Problem 2.a: Calculate the volume and then the area. The prism has dimensions: Length = 4 units, Width = 3 units, Height = 3 units. Volume: V = 4 units × 3 units × 3 units V = 36 cubic units Surface Area: SA = 2(4 × 3 + 4 × 3 + 3 × 3) SA = 2(12 + 12 + 9) SA = 2(33) SA = 66 square units Problem 1.c: For 3 cubic units x 3 cubic units x 4 cubic units: Volume: V = 3 units × 3 units × 4 units V = 36 cubic units Surface Area: SA = 2(3 × 3 + 3 × 4 + 3 × 4) SA = 2(9 + 12 + 12) SA = 2(33) SA = 66 square units Problem 1.d: For 5 cubic units x 6 cubic units x 4 cubic units: Volume: V = 5 units × 6 units × 4 units V = 120 cubic units Surface Area: SA = 2(5 × 6 + 5 × 4 + 6 × 4) SA = 2(30 + 20 + 24) SA = 2(74) SA = 148 square units Problem 1.e: For 7 cubic units x 8 cubic units x 9 cubic units: Volume: V = 7 units × 8 units × 9 units V = 504 cubic units Surface Area: SA = 2(7 × 8 + 7 × 9 + 8 × 9) SA = 2(56 + 63 + 72) SA = 2(191) SA = 382 square units Problem 1.f: For 4 cubic units x 8 cubic units x 12 cubic units: Volume: V = 4 units × 8 units × 12 units V = 384 cubic units Surface Area: SA = 2(4 × 8 + 4 × 12 + 8 × 12) SA = 2(32 + 48 + 96) SA = 2(176) SA = 352 square units Millimetre fun: What will the surface area in square units be of a rectangular prism with 6 cubic units by 4 cubic units by 3 units? Dimensions: Length = 6 units, Width = 4 units, Height = 3 units. Surface Area: SA = 2(6 × 4 + 6 × 3 + 4 × 3) SA = 2(24 + 18 + 12) SA = 2(54) SA = 108 square units That's 2 down. 3 left today — send the next one.