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 for question 4, as indicated in your image: 4. Find the volume and surface of the following a) sphere radius 3.5 cm Volume of a sphere: V = (4)/(3) r^3 Surface area of a sphere: SA = 4 r^2 Given r = 3.5 cm. Step 1: Calculate the volume. V = (4)/(3) × × (3.5 cm)^3 V = (4)/(3) × × 42.875 cm^3 V ≈ 179.59 cm^3 Step 2: Calculate the surface area. SA = 4 × × (3.5 cm)^2 SA = 4 × × 12.25 cm^2 SA ≈ 153.94 cm^2 The volume is 179.59 cm^3 and the surface area is 153.94 cm^2. b) cone radius 7 cm and slant height 10 cm Volume of a cone: V = (1)/(3) r^2 h Surface area of a cone: SA = r (r+l) Given r = 7 cm and l = 10 cm. Step 1: Find the height h using the Pythagorean theorem: h = sqrt(l^2 - r^2). h = sqrt((10 cm))^2 - (7 cm)^2 h = sqrt(100 cm)^2 - 49 cm^2 h = sqrt(51) cm ≈ 7.14 cm Step 2: Calculate the volume. V = (1)/(3) × × (7 cm)^2 × sqrt(51) cm V = (1)/(3) × × 49 cm^2 × 7.1414 cm V ≈ 366.49 cm^3 Step 3: Calculate the surface area. SA = × 7 cm × (7 cm + 10 cm) SA = × 7 cm × 17 cm SA = 119 cm^2 SA ≈ 373.85 cm^2 The volume is 366.49 cm^3 and the surface area is 373.85 cm^2. c) cuboid of 5 m x 2 m x 3.2 m Volume of a cuboid: V = lwh Surface area of a cuboid: SA = 2(lw + lh + wh) Given l = 5 m, w = 2 m, h = 3.2 m. Step 1: Calculate the volume. V = 5 m × 2 m × 3.2 m V = 32 m^3 Step 2: Calculate the surface area. SA = 2((5 m × 2 m) + (5 m × 3.2 m) + (2 m × 3.2 m)) SA = 2(10 m^2 + 16 m^2 + 6.4 m^2) SA = 2(32.4 m^2) SA = 64.8 m^2 The volume is 32 m^3 and the surface area is 64.8 m^2. d) cube of sides 4 m Volume of a cube: V = s^3 Surface area of a cube: SA = 6s^2 Given s = 4 m. Step 1: Calculate the volume. V = (4 m)^3 V = 64 m^3 Step 2: Calculate the surface area. SA = 6 × (4 m)^2 SA = 6 × 16 m^2 SA = 96 m^2 The volume is 64 m^3 and the surface area is 96 m^2. Last free one today — make it count tomorrow, or type /upgrade for unlimited.