Mensuration — Flashcards
Telangana Board · Class 10 · Mathematics
22 flashcards for Mensuration (Telangana Board Class 10 Mathematics) to test yourself on key terms and facts. Sample: "Solve: Find the slant height.
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Solve: Find the slant height of a conical tent with radius 7 m and height 10 m.
Answer
Step 1: Use the formula l = √(r^2 + h^2). Step 2: Substitute r = 7 m and h = 10 m. l = √(7^2 + 10^2) = √(49 + 100) = √149. Step 3: √149 ≈ 12.2 m. Answer: The slant height is 12.2 m.
A conical tent has radius 7 m, height 10 m, and canvas width 2 m. Find the length of canvas needed.
Answer
Step 1: Find slant height. l = √(7^2 + 10^2) = √149 ≈ 12.2 m. Step 2: Find curved surface area of the cone. CSA = πrl = (22/7) × 7 × 12.2 = 268.4 m². Step 3: Length of canvas = area ÷ width = 268.4 ÷ …
Find the total surface area of a cylinder with radius 14 cm and height 21 cm.
Answer
Step 1: Use TSA of cylinder = 2πr(r + h). Step 2: Substitute r = 14 cm and h = 21 cm. TSA = 2 × (22/7) × 14 × (14 + 21) = 2 × (22/7) × 14 × 35 = 3080 cm². Answer: Total surface area = 3080 cm².
A cylinder has radius 14 cm and height 21 cm. Find its base area, curved surface area, total surface area, and volume.
Answer
Step 1: Base area = πr² = (22/7) × 14² = 616 cm². Step 2: CSA = 2πrh = 2 × (22/7) × 14 × 21 = 1848 cm². Step 3: TSA = 2 × base area + CSA = 2 × 616 + 1848 = 3080 cm². Step 4: Volume = πr²h = 616 × 21 …
Find the surface area and volume of a sphere of radius 2.1 cm.
Answer
Step 1: Surface area of sphere = 4πr². = 4 × (22/7) × (2.1)² = 55.44 cm². Step 2: Volume of sphere = (4/3)πr³. = (4/3) × (22/7) × (2.1)³ = 38.808 cm³. Answer: Surface area = 55.44 cm² and volume = 38.
Find the volume and total surface area of a hemisphere of radius 3.5 cm.
Answer
Step 1: Volume of hemisphere = (2/3)πr³. = (2/3) × (22/7) × (3.5)³ = 89.83 cm³. Step 2: TSA of hemisphere = 3πr². = 3 × (22/7) × (3.5)² = 115.5 cm². Answer: Volume = 89.83 cm³ and TSA = 115.5 cm².
When do you use CSA = 2πrh for a cylinder? Give a quick example.
Answer
Use CSA = 2πrh when only the curved side of the cylinder is needed, not the two circular bases. Example: For radius 1 m and height 7 m, CSA = 2 × π × 1 × 7 = 14π m² = 44 m² if π = 22/7. Answer: This f…
Why is the total surface area of a cone on a cylinder not equal to the sum of the two total surface areas?
Answer
When two solids are joined, the touching surfaces disappear from outside view. So, the hidden circular face is not counted again. For a combined solid, only the exposed surfaces are added. Example ide…
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