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
Step 1: Calculate the volume of the timber cube. The side length of the cube is 12 cm. The formula for the volume of a cube is V_cube = s^3. V_cube = (12 cm)^3 V_cube = 1728 cm^3 Step 2: Calculate the area of the trapezoidal cross-section. The parallel sides of the trapezoid are a = 8.7 cm and b = 6.4 cm. The height of the trapezoid is h = 5.8 cm. The formula for the area of a trapezoid is A_trapezoid = (1)/(2)(a+b)h. A_trapezoid = (1)/(2)(8.7 cm + 6.4 cm)(5.8 cm) A_trapezoid = (1)/(2)(15.1 cm)(5.8 cm) A_trapezoid = (15.1 cm)(2.9 cm) A_trapezoid = 43.79 cm^2 Step 3: Calculate the volume of the trapezoidal prism. The length of the prism is L = 12 cm. The formula for the volume of a prism is V_prism = A_base × L. V_prism = (43.79 cm^2)(12 cm) V_prism = 525.48 cm^3 Step 4: Calculate the volume of timber left in the cube. The volume of timber left is the volume of the cube minus the volume of the prism. V_left = V_cube - V_prism V_left = 1728 cm^3 - 525.48 cm^3 V_left = 1202.52 cm^3 The volume of the timber left in the cube is 1202.52 cm^3.