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: Identify the given information and the shape. The figure shows a pyramid with apex A and base BCDE. The height of the pyramid is given as h = 11 \, cm. The base is a quadrilateral with side lengths CD = 10 \, cm and ED = 7 \, cm. We will assume the base BCDE is a rectangle, with CD and ED as its adjacent sides. Step 2: Calculate the area of the base. For a rectangular base, the area is the product of its length and width. Base Area = CD × ED Base Area = 10 \, cm × 7 \, cm Base Area = 70 \, cm^2 Step 3: State the correct formula for the volume of a pyramid. The formula provided in the question, V = (1)/(2) × base area + height, is incorrect for calculating the volume of a pyramid. This formula would result in adding an area to a length, which does not yield a volume. The correct formula for the volume of a pyramid is: V = (1)/(3) × Base Area × height Step 4: Substitute the calculated base area and given height into the correct volume formula and compute the volume. V = (1)/(3) × 70 \, cm^2 × 11 \, cm V = (770)/(3) \, cm^3 V ≈ 256.67 \, cm^3 The volume of the pyramid is 256.67 cm^3. Send me the next one 📸