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 are the solutions to the remaining questions. Question 20: Calculate the volume of these solids (8 marks) a) Cone Step 1: Identify the given dimensions. Radius r = 3.5\, cm Height h = 10\, cm Step 2: Use the formula for the volume of a cone. V = (1)/(3) r^2 h Using = (22)/(7): V = (1)/(3) × (22)/(7) × (3.5\, cm)^2 × 10\, cm V = (1)/(3) × (22)/(7) × 12.25\, cm^2 × 10\, cm V = (1)/(3) × 22 × 1.75\, cm^2 × 10\, cm V = (1)/(3) × 385\, cm^3 V = 128.33\, cm^3 The volume of the cone is 128.33 cm^3. b) Cube Step 1: Identify the given dimension. Side length s = 5\, cm Step 2: Use the formula for the volume of a cube. V = s^3 V = (5\, cm)^3 V = 125\, cm^3 The volume of the cube is 125 cm^3. c) Cuboid Step 1: Identify the given dimensions. Length l = 8\, cm Width w = 4\, cm Height h = 2\, cm Step 2: Use the formula for the volume of a cuboid. V = l × w × h V = 8\, cm × 4\, cm × 2\, cm V = 64\, cm^3 The volume of the cuboid is 64 cm^3. d) Cylinder Step 1: Identify the given dimensions. Radius r = 7\, cm Height h = 10\, cm Step 2: Use the formula for the volume of a cylinder. V = r^2 h Using = (22)/(7): V = (22)/(7) × (7\, cm)^2 × 10\, cm V = (22)/(7) × 49\, cm^2 × 10\, cm V = 22 × 7\, cm^2 × 10\, cm V = 1540\, cm^3 The volume of the cylinder is 1540 cm^3. Question 31: Find the Surface area of a Sphere of radius 7cm. 2 marks Step 1: Identify the given dimension. Radius r = 7\, cm Step 2: Use the formula for the surface area of a sphere. A = 4 r^2 Using = (22)/(7): A = 4 × (22)/(7) × (7\, cm)^2 A = 4 × (22)/(7) × 49\, cm^2 A = 4 × 22 × 7\, cm^2 A = 88 × 7\, cm^2 A = 616\, cm^2 The surface area of the sphere is 616 cm^2. Question 32: Find the Surface of a Cuboid. 8cm x 6cm x 4cm. 2 marks Step 1: Identify the given dimensions. Length l = 8\, cm Width w = 6\, cm Height h = 4\, cm Step 2: Use the formula for the surface area of a cuboid. A = 2(lw + lh + wh) A = 2((8\, cm × 6\, cm) + (8\, cm × 4\, cm) + (6\, cm × 4\, cm)) A = 2(48\, cm^2 + 32\, cm^2 + 24\, cm^2) A = 2(104\, cm^2) A = 208\, cm^2 The surface area of the cuboid is 208 cm^2. Question 10: A hemisphere bowl of radius 14cm is to be painted. Assuming the question asks for the surface area of the outer curved surface of the open hemisphere bowl. Step 1: Identify the given dimension. Radius r = 14\, cm Step 2: Use the formula for the curved surface area of a hemisphere. A = 2 r^2 Using = (22)/(7): A = 2 × (22)/(7) × (14\, cm)^2 A = 2 × (22)/(7) × 196\, cm^2 A = 2 × 22 × 28\, cm^2 A = 44 × 28\, cm^2 A = 1232\, cm^2 The surface area to be painted is 1232 cm^2. Last free one today — make it count tomorrow, or type /upgrade for unlimited.