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 Mina — missed you this week. Here's the solution to question 12: a) To find the area of the triangular surfaces (Lateral Surface Area) of a square-based pyramid, the formula is: LSA = 2al where a is the length of the base side and l is the slant height. b) We are given the length of a side of the base a = 12 ft and the area of the triangular surfaces (LSA) = 240 sq. ft. We use the formula from part (a) to find the slant height l. Step 1: Write the formula for Lateral Surface Area (LSA). LSA = 2al Step 2: Substitute the given values into the formula. 240 = 2 × 12 × l Step 3: Solve for l. 240 = 24l l = (240)/(24) l = 10 ft The slant height of the tent is 10 ft. c) To find how many tourists can be accommodated, we first need to calculate the volume of the tent. We are given that 64 cu. ft. of air is required per tourist. Step 1: Calculate the vertical height (h) of the pyramid using the slant height (l) and half of the base side length ((a)/(2)). We know l = 10 ft and a = 12 ft. Using the Pythagorean theorem: l^2 = h^2 + ((a)/(2))^2 10^2 = h^2 + ((12)/(2))^2 100 = h^2 + 6^2 100 = h^2 + 36 h^2 = 100 - 36 h^2 = 64 h = sqrt(64) h = 8 ft Step 2: Calculate the volume (V) of the pyramid. The formula for the volume of a pyramid is: V = (1)/(3) × Base Area × h The base is a square with side length a = 12 ft, so Base Area = a^2 = 12^2 = 144 sq. ft. V = (1)/(3) × 144 ft^2 × 8 ft V = 48 × 8 ft^3 V = 384 ft^3 Step 3: Calculate the number of tourists that can be accommodated. Each tourist requires 64 cu. ft. of air. Number of tourists = Total VolumeAir required per tourist Number of tourists = 384 ft^364 ft^3/tourist Number of tourists = 6 The tent can accommodate 6 tourists. Send me the next one 📸