Calculate the area of a trapezium with parallel sides 0.05 m and 9 cm and height 6 cm. Also, find the total surface area and volume of a cone with slant height 13 cm and radius 5 cm.

Here are the solutions for Question Four: Question Four a) Calculate the area of the trapezium whose parallel sides are 0.05 m and 9 cm with an height of 6 cm. Step 1: Convert all units to centimeters. The parallel sides are a = 0.05 m and b = 9 cm. The height is h = 6 cm. a = 0.05 m = 0.05 × 100 cm = 5 cm Step 2: Use the formula for the area of a trapezium. The area A of a trapezium is given by A = (1)/(2)(a+b)h. A = (1)/(2)(5 cm + 9 cm)(6 cm) A = (1)/(2)(14 cm)(6 cm) A = (7 cm)(6 cm) A = 42 cm^2 b) A cone has a slant height of 13 cm with a radius of 5 cm for its circular base. Calculate: i. Total surface area ii. Volume Given: Slant height l = 13 cm, radius r = 5 cm. Use = (22)/(7). i. Total surface area Step 1: Use the formula for the total surface area of a cone. The total surface area A_total of a cone is given by A_total = r (r+l). A_total = (22)/(7) × 5 cm × (5 cm + 13 cm) A_total = (22)/(7) × 5 cm × 18 cm A_total = (1980)/(7) cm^2 A_total ≈ 282.86 cm^2 ii. Volume Step 1: Calculate the perpendicular height h of the cone using the Pythagorean theorem. h^2 + r^2 = l^2 h^2 + (5 cm)^2 = (13 cm)^2 h^2 + 25 cm^2 = 169 cm^2 h^2 = 169 cm^2 - 25 cm^2 h^2 = 144 cm^2 h = sqrt(144 cm)^2 h = 12 cm Step 2: Use the formula for the volume of a cone. The volume V of a cone is given by V = (1)/(3) r^2 h. V = (1)/(3) × (22)/(7) × (5 cm)^2 × 12 cm V = (1)/(3) × (22)/(7) × 25 cm^2 × 12 cm V = (22 × 25 × 12)/(3 × 7) cm^3 V = (6600)/(21) cm^3 V = (2200)/(7) cm^3 V ≈ 314.29 cm^3 c) Calculate the volume of the cylinder whose height is 7 cm and a diameter of 28 cm. Given: Height h = 7 cm, diameter D = 28 cm. Use = (22)/(7). Step 1: Calculate the radius r of the cylinder. r = (D)/(2) = 28 cm2 = 14 cm Step 2: Use the formula for the volume of a cylinder. The volume V of a cylinder is given by V = r^2 h. V = (22)/(7) × (14 cm)^2 × 7 cm V = (22)/(7) × 196 cm^2 × 7 cm V = 22 × 196 cm^3 V = 4312 cm^3 d) Solve the following simultaneous equation using the elimination method. x+y=3 (1) x+y-3=9 (2) Step 1: Simplify equation (2). x+y-3=9 x+y=9+3 x+y=12 (3) Step 2: Use the elimination method by subtracting equation (1) from equation (3). (x+y) - (x+y) = 12 - 3 0 = 9 Step 3: Interpret the result. Since 0=9 is a false statement, the system of equations is inconsistent. This means there is no solution that satisfies both equations simultaneously. The system has no solution. Send me the next one 📸