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.
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Here is the solution for question 1 and 2: The image shows a prism with a trapezoidal base. From the diagram, the top parallel side is 16 cm, the height of the trapezoid is 17 cm, and the length of the prism is 60 cm. The bottom parallel side is marked as 'x'. By observing the grid, the top side is 8 grid units and the bottom side is 12 grid units. Since 16 cm corresponds to 8 units, then 1 unit = 2 cm. Thus, the bottom parallel side x = 12 × 2 cm = 24 cm. Part a) What is its volume when full? Step 1: Calculate the area of the trapezoidal base. The formula for the area of a trapezoid is A = (1)/(2)(a+b)h, where a and b are the lengths of the parallel sides and h is the perpendicular height. Here, a = 16 cm, b = 24 cm, and h = 17 cm. A_base = (1)/(2)(16 cm + 24 cm)(17 cm) A_base = (1)/(2)(40 cm)(17 cm) A_base = 20 cm × 17 cm A_base = 340 cm^2 Step 2: Calculate the volume of the prism when full. The formula for the volume of a prism is V = A_base × Length. Here, A_base = 340 cm^2 and Length = 60 cm. V_full = 340 cm^2 × 60 cm V_full = 20400 cm^3 The volume when full is 20400 cm^3 Part b) Find the capacity in litres when half full. Step 1: Calculate the volume when the prism is half full. V_half = (1)/(2) × V_full V_half = (1)/(2) × 20400 cm^3 V_half = 10200 cm^3 Step 2: Convert the volume from cubic centimetres to litres. We know that 1 litre = 1000 cm^3. Capacity in litres = V_half1000 cm^3/litre Capacity in litres = 10200 cm^31000 cm^3/litre Capacity in litres = 10.2 litres The capacity when half full is 10.2 litres Last free one today — make it count tomorrow, or type /upgrade for unlimited.