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's the solution for Question 9: a) Step 1: Identify the given diameter. The diameter of the sphere is 14 cm. Step 2: Calculate the radius. The radius (r) is half of the diameter. r = diameter2 r = 14 cm2 r = 7 cm The radius of the sphere is 7 cm. b) Step 1: Identify the radius. The radius is r = 7 cm. Step 2: Substitute the radius into the surface area formula for a sphere. SA = 4 r^2 SA = 4 × × (7 cm)^2 SA = 4 × × 49 cm^2 SA = 196 cm^2 SA ≈ 196 × 3.14159265... cm^2 SA ≈ 615.75216 cm^2 Step 3: Round the surface area to 2 decimal places. SA = 615.75 cm^2 The surface area of the sphere is 615.75 cm^2. c) Step 1: Identify the radius. The radius is r = 7 cm. Step 2: Substitute the radius into the volume formula for a sphere. V = (4)/(3) r^3 V = (4)/(3) × × (7 cm)^3 V = (4)/(3) × × 343 cm^3 V = (1372)/(3) cm^3 V ≈ (1372)/(3) × 3.14159265... cm^3 V ≈ 457.3333... × 3.14159265... cm^3 V ≈ 1436.75504 cm^3 Step 3: Round the volume to 2 decimal places. V = 1436.76 cm^3 The volume of the sphere is 1436.76 cm^3. d) Step 1: Identify the radius. The radius is r = 7 cm. Step 2: Substitute the radius into the total surface area formula for a hemisphere. TSA of hemisphere = 3 r^2 TSA of hemisphere = 3 × × (7 cm)^2 TSA of hemisphere = 3 × × 49 cm^2 TSA of hemisphere = 147 cm^2 TSA of hemisphere ≈ 147 × 3.14159265... cm^2 TSA of hemisphere ≈ 461.81412 cm^2 Step 3: Round the total surface area to 2 decimal places. TSA of hemisphere = 461.81 cm^2 The total surface area of the hemisphere is 461.81 cm^2. Last free one today — make it count tomorrow, or type /upgrade for unlimited.