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.
ScanSolve AI Answer
(a) r = 7 cm, h = 10 cm Step 1: Curved surface area (CSA) = 2 rh Substitute the values: 2 × 7 × 10 = 140 cm² Step 2: Total surface area (TSA) = 2 r(h + r) 2 × 7 × (10 + 7) = 2 × 7 × 17 = 238 cm² Step 3: Volume (V) = r^2 h × 7^2 × 10 = × 49 × 10 = 490 cm³ 140 cm², 238 cm², 490 cm³ (b) r = 2.5 cm = (5)/(2) cm, h = 7 cm Step 1: CSA = 2 rh 2 × (5)/(2) × 7 = 2 × (35)/(2) = 35 cm² Step 2: TSA = 2 r(h + r) h + r = 7 + (5)/(2) = (19)/(2) 2 × (5)/(2) × (19)/(2) = 2 × (95)/(4) = (95)/(2) cm² Step 3: V = r^2 h r^2 = ((5)/(2))^2 = (25)/(4) × (25)/(4) × 7 = × (175)/(4) = (175)/(4) cm³ 35 cm², (95)/(2) cm², (175)/(4) cm³ (c) Circumference of base = 14 cm, h = 10 cm Step 1: Circumference = 2 r = 14 r = (14)/(2) = (7)/() cm Step 2: TSA = 2 r(h + r) h + r = 10 + (7)/() 2 × (7)/() × (10 + (7)/()) = 14 × (10 + (7)/()) = 140 + (98)/() cm² r = (7)/() cm, TSA = 140 + (98)/() cm² (d) r + h = 24 cm, h = 21 cm (from diagram) Step 1: r = 24 - 21 = 3 cm Step 2: CSA = 2 rh 2 × 3 × 21 = 126 cm² Step 3: TSA = 2 r(h + r) h + r = 21 + 3 = 24 2 × 3 × 24 = 144 cm² CSA = 126 cm², TSA = 144 cm²