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
Welcome back birajlimbu848 — missed you this week. Here's the solution to question number 5: Given: Vertical height of a square-based pyramid, h = 24 cm Length of one side of base, a = 14 cm a) The formula to find the volume of a square-based pyramid is: V = (1)/(3) × base area × height Since the base is a square with side length a, the base area is a^2. So, the formula is: V = (1)/(3) a^2 h b) To find the total surface area of the pyramid, we first need to calculate the slant height (l). Step 1: Calculate the slant height (l). The slant height can be found using the Pythagorean theorem: l = sqrt(h^2 + ((a)/(2))^2) l = sqrt(24^2 + ((14)/(2))^2) l = sqrt(24^2 + 7^2) l = sqrt(576 + 49) l = sqrt(625) l = 25 cm Step 2: Calculate the total surface area (TSA). The total surface area is the sum of the base area and the lateral surface area. TSA = Base Area + Lateral Surface Area TSA = a^2 + 2al TSA = 14^2 + 2 × 14 × 25 TSA = 196 + 700 TSA = 896 cm^2 c) To find the volume of the pyramid: Step 1: Use the formula for the volume of a square-based pyramid. V = (1)/(3) a^2 h Step 2: Substitute the given values and calculate. V = (1)/(3) × 14^2 × 24 V = (1)/(3) × 196 × 24 V = 196 × 8 V = 1568 cm^3 Send me the next one 📸