Mensuration — Telangana (SSC) Class 10 Mathematics Solutions (Free)

Step 1: Side of cube a = 5 cm Step 2: Volume V = a³ = 5³ = 125 cm³ Step 3: Surface area SA = 6a² = 6 × 5² = 6 × 25 = 150 cm² Final Answer: Volume = 125 cm³; Surface area = 150 cm²

Step 1: Radius r = 3 cm, height h = 7 cm Step 2: Volume V = πr²h = π × 3² × 7 = 63π cm³ ≈ 197.92 cm³ Step 3: Curved surface area = 2πrh = 2π × 3 × 7 = 42π cm² ≈ 131.95 cm² Step 4: Total surface area = 2πr² + 2πrh = 2πr(r + h) = 2π × 3(3 + 7) = 60π cm² ≈ 188.5 cm² Final Answer: Volume = 63π cm³ ≈ 197.92 cm³; Total surface area = 60π cm² ≈ 188.5 cm²

Step 1: Radius r = 4 cm, height h = 9 cm Step 2: Volume V = (1/3)πr²h = (1/3) × π × 4² × 9 Step 3: V = (1/3) × π × 16 × 9 = 48π cm³ Step 4: V ≈ 48 × 3.14159 ≈ 150.8 cm³ Final Answer: Volume = 48π cm³ ≈ 150.8 cm³

Step 1: Radius r = 6 cm Step 2: Volume V = (4/3)πr³ = (4/3) × π × 6³ = (4/3) × π × 216 Step 3: V = 288π cm³ ≈ 904.78 cm³ Step 4: Surface area SA = 4πr² = 4π × 6² = 4π × 36 = 144π cm² Step 5: SA ≈ 452.39 cm² Final Answer: Volume = 288π cm³ ≈ 904.78 cm³; Surface area = 144π cm² ≈ 452.39 cm²

Step 1: Length l = 8 cm, width w = 5 cm, height h = 3 cm Step 2: Volume V = l × w × h = 8 × 5 × 3 = 120 cm³ Step 3: Surface area SA = 2(lw + wh + lh) Step 4: SA = 2(8×5 + 5×3 + 8×3) = 2(40 + 15 + 24) = 2 × 79 = 158 cm² Final Answer: Volume = 120 cm³; Surface area = 158 cm²