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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Okay, scoddyevarau87@gmail.com, let's work through these geometry problems. Problem 29: Calculate the volume of these solids. a) Cone Step 1: Write the formula for the volume of a cone. V = (1)/(3) r^2 h Step 2: Substitute the given values. Given r = 3.5 cm and h = 10 cm. Use = (22)/(7). V = (1)/(3) × (22)/(7) × (3.5 cm)^2 × 10 cm V = (1)/(3) × (22)/(7) × (3.5 × 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) × 38.5 cm^2 × 10 cm V = (385)/(3) cm^3 V ≈ 128.33 cm^3 b) Cube Step 1: Write the formula for the volume of a cube. V = s^3 Step 2: Substitute the given value. Given side s = 5 cm. V = (5 cm)^3 V = 5 × 5 × 5 cm^3 V = 125 cm^3 c) Cuboid Step 1: Write the formula for the volume of a cuboid. V = lwh Step 2: Substitute the given values. Given length l = 8 cm, width w = 4 cm, and height h = 2 cm. V = 8 cm × 4 cm × 2 cm V = 32 cm^2 × 2 cm V = 64 cm^3 d) Cylinder Step 1: Write the formula for the volume of a cylinder. V = r^2 h Step 2: Substitute the given values. Given r = 7 cm and h = 10 cm. Use = (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 = 154 cm^2 × 10 cm V = 1540 cm^3 Problem 30: A rectangular tank measures 6 metres × 5 metres × 4 metres. How many litres of water can it hold? Step 1: Calculate the volume of the tank in cubic metres. V = lwh V = 6 m × 5 m × 4 m V = 30 m^2 × 4 m V = 120 m^3 Step 2: Convert the volume from cubic metres to litres. We know that 1 m^3 = 1000 litres. V_litres = 120 m^3 × 1000 litres1 m^3 V_litres = 120000 litres Problem 31: Find the surface area of a sphere of radius 7 cm. Step 1: Write the formula for the surface area of a sphere. A = 4 r^2 Step 2: Substitute the given values. Given r = 7 cm. Use = (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 Problem 32: Find the surface area of a cuboid 8 cm × 6 cm × 4 cm. Step 1: Write the formula for the surface area of a cuboid. A = 2(lw + lh + wh) Step 2: Substitute the given values. Given length l = 8 cm, width w = 6 cm, and height h = 4 cm. 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 Problem 10: A hemisphere bowl of radius 14 cm is to be painted. Assuming the bowl is open, only the curved surface area needs to be painted. Step 1: Write the formula for the curved surface area of a hemisphere. A = 2 r^2 Step 2: Substitute the given values. Given r = 14 cm. Use = (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 3 done, 2 left today. You're making progress.