Mensuration — Flashcards
Tamil Nadu Board · Class 10 · Mathematics
40 flashcards for Mensuration (Tamil Nadu Board Class 10 Mathematics) to test yourself on key terms and facts.
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Find the curved surface area of a cylinder with radius 7 cm and height 10 cm.
Answer
Formula: C.S.A. = 2πrh Given: r = 7 cm, h = 10 cm Step 1: C.S.A. = 2 × (22/7) × 7 × 10 Step 2: C.S.A. = 2 × 22 × 10 Step 3: C.S.A. = 440 cm² Answer: 440 cm²…
Formula for total surface area of a cylinder
Answer
T.S.A. of cylinder = 2πr(h + r) square units Where: - r = radius of the base - h = height of the cylinder - π ≈ 22/7 or 3.14 Example: For r = 5 cm, h = 12 cm T.S.A. = 2π(5)(12 + 5) = 2π(5)(17) = 170…
A cylindrical drum has height 20 cm and base radius 14 cm. Find its total surface area.
Answer
Formula: T.S.A. = 2πr(h + r) Given: h = 20 cm, r = 14 cm Step 1: T.S.A. = 2 × (22/7) × 14 × (20 + 14) Step 2: T.S.A. = 2 × (22/7) × 14 × 34 Step 3: T.S.A. = 2 × 22 × 2 × 34 Step 4: T.S.A. = 2992 cm² A…
The curved surface area of a cylinder is 88 cm² and height is 14 cm. Find the diameter.
Answer
Formula: C.S.A. = 2πrh Given: C.S.A. = 88 cm², h = 14 cm Step 1: 88 = 2 × (22/7) × r × 14 Step 2: 88 = 2 × 22 × r × 2 Step 3: 88 = 88r Step 4: r = 1 cm Step 5: Diameter = 2r = 2 cm Answer: 2 cm…
A garden roller of length 3 m and diameter 2.8 m covers what area in 8 revolutions?
Answer
Concept: One revolution = curved surface area of cylinder Given: Length h = 3 m, Diameter d = 2.8 m, Radius r = 1.4 m Step 1: Area in 1 revolution = C.S.A. = 2πrh Step 2: Area = 2 × (22/7) × 1.4 × 3 S…
Formula for curved surface area of a right circular cone
Answer
C.S.A. of cone = πrl square units Where: - r = radius of the base - l = slant height = √(h² + r²) - h = height of the cone Example: For r = 5 cm, h = 12 cm First find l: l = √(144 + 25) = √169 = 13 …
A conical tent has radius 7 m and height 24 m. Calculate the length of canvas needed if canvas width is 4 m.
Answer
Step 1: Find slant height l = √(r² + h²) = √(49 + 576) = √625 = 25 m Step 2: C.S.A. = πrl = (22/7) × 7 × 25 = 550 m² Step 3: Length of canvas = Area ÷ Width = 550 ÷ 4 = 137.5 m Answer: 137.5 m of canv…
Formula for total surface area of a cone
Answer
T.S.A. of cone = πr(l + r) square units Alternatively: T.S.A. = πrl + πr² Where: - r = radius of the base - l = slant height - π ≈ 22/7 Example: For r = 7 cm, l = 25 cm T.S.A. = (22/7) × 7 × (25 + 7…
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