Mensuration — Telangana (SSC) Class 10 Mathematics Solutions (Free)
Free step-by-step Telangana (SSC) Class 10 Mathematics solutions for "Mensuration" — important questions with detailed answers, download PDF for board exam preparation.
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Mensuration — Textbook Questions Answered (8)
Q1: Find the volume and surface area of a cube with side 5 cm.
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
Q2: Find the volume and surface area of a cylinder with radius 3 cm and height 7 cm.
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
Q3: Find the volume of a cone with radius 4 cm and height 9 cm.
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
Q4: Find the volume and surface area of a sphere with radius 6 cm.
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
Q5: A rectangular prism (cuboid) has dimensions 8 cm × 5 cm × 3 cm. Find its volume and total surface area.
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
Q6: A hemisphere has radius 7 cm. Find its volume and total surface area.
Step 1: Radius r = 7 cm
Step 2: Volume of hemisphere = (2/3)πr³ = (2/3) × π × 7³ = (2/3) × π × 343
Step 3: V = (686/3)π cm³ ≈ 718.4 cm³
Step 4: Curved surface area = 2πr² = 2π × 49 = 98π cm²
Step 5: Base area = πr² = π × 49 = 49π cm²
Step 6: Total surface area = 98π + 49π = 147π cm² ≈ 461.81 cm²
Final Answer: Volume = (686/3)π cm³ ≈ 718.4 cm³; Surface area = 147π cm² ≈ 461.81 cm²
Q7: Find the slant height of a cone if its radius is 5 cm and height is 12 cm. Also find curved surface area.
Step 1: Radius r = 5 cm, height h = 12 cm
Step 2: Slant height l = √(r² + h²) = √(5² + 12²) = √(25 + 144) = √169 = 13 cm
Step 3: Curved surface area = πrl = π × 5 × 13 = 65π cm²
Step 4: CSA ≈ 204.20 cm²
Final Answer: Slant height = 13 cm; Curved surface area = 65π cm² ≈ 204.20 cm²
Q8: A solid consists of a cylinder of radius 3 cm and height 6 cm with a cone of same radius and height 4 cm on top. Find total volume.
Step 1: Volume of cylinder = πr²h = π × 3² × 6 = 54π cm³
Step 2: Volume of cone = (1/3)πr²h = (1/3) × π × 3² × 4 = 12π cm³
Step 3: Total volume = 54π + 12π = 66π cm³
Step 4: Total volume ≈ 207.35 cm³
Final Answer: Total volume = 66π cm³ ≈ 207.35 cm³
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