Surface areas and Volumes — Flashcards
Telangana Board · Class 9 · Mathematics
20 flashcards for Surface areas and Volumes (Telangana Board Class 9 Mathematics) to test yourself on key terms and facts.
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Find the total surface area of a cuboid with length 8 cm, breadth 6 cm, and height 4 cm.
Answer
Formula: TSA = 2(lb + bh + lh) Step 1: Calculate each face area - lb = 8 × 6 = 48 cm² - bh = 6 × 4 = 24 cm² - lh = 8 × 4 = 32 cm² Step 2: TSA = 2(48 + 24 + 32) = 2(104) = 208 cm² Answer: 208 cm²…
A cube has edge length 5 cm. Find its volume and total surface area.
Answer
Given: Edge = 5 cm Volume: V = a³ = 5³ = 125 cm³ TSA: TSA = 6a² = 6 × 5² = 6 × 25 = 150 cm² Answer: Volume = 125 cm³, TSA = 150 cm²…
Find the curved surface area of a cylinder with radius 7 cm and height 10 cm.
Answer
Formula: CSA = 2πrh Given: r = 7 cm, h = 10 cm Step 1: CSA = 2 × (22/7) × 7 × 10 Step 2: CSA = 2 × 22 × 10 = 440 cm² Answer: 440 cm²…
A cylindrical tank has diameter 14 m and height 8 m. Find its total surface area.
Answer
Given: d = 14 m, so r = 7 m, h = 8 m Formula: TSA = 2πr(r + h) Step 1: TSA = 2 × (22/7) × 7 × (7 + 8) Step 2: TSA = 2 × 22 × 15 = 660 m² Answer: 660 m²…
Find the volume of a cylinder with radius 3.5 cm and height 12 cm.
Answer
Formula: V = πr²h Given: r = 3.5 cm, h = 12 cm Step 1: V = (22/7) × (3.5)² × 12 Step 2: V = (22/7) × 12.25 × 12 Step 3: V = 22 × 1.75 × 12 = 462 cm³ Answer: 462 cm³…
A cone has radius 4 cm and height 3 cm. Find its slant height and curved surface area.
Answer
Given: r = 4 cm, h = 3 cm Step 1: Find slant height using l² = r² + h² l² = 4² + 3² = 16 + 9 = 25 l = 5 cm Step 2: CSA = πrl = (22/7) × 4 × 5 = 440/7 ≈ 62.86 cm² Answer: Slant height = 5 cm, CSA = 440…
Find the total surface area of a cone with radius 7 cm and slant height 25 cm.
Answer
Formula: TSA = πr(r + l) Given: r = 7 cm, l = 25 cm Step 1: TSA = (22/7) × 7 × (7 + 25) Step 2: TSA = 22 × 32 = 704 cm² Answer: 704 cm²…
A cone has volume 154 cm³ and base radius 7 cm. Find its height.
Answer
Formula: V = (1/3)πr²h Given: V = 154 cm³, r = 7 cm Step 1: 154 = (1/3) × (22/7) × 7² × h Step 2: 154 = (1/3) × 22 × 7 × h Step 3: 154 = (154h)/3 Step 4: h = 3 cm Answer: Height = 3 cm…
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