Surface areas and Volumes — Flashcards
Karnataka Board · Class 9 · Mathematics
20 flashcards for Surface areas and Volumes (Karnataka Board Class 9 Mathematics) to test yourself on key terms and facts.
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Find the curved surface area of a cone with base radius 7 cm and slant height 15 cm.
Answer
Formula: Curved Surface Area = πrl Step 1: Identify given values → r = 7 cm, l = 15 cm Step 2: Apply formula → CSA = π × 7 × 15 Step 3: Calculate → CSA = (22/7) × 7 × 15 = 22 × 15 = 330 cm² Answer: 33…
A cone has height 12 cm and base radius 5 cm. Find its slant height and curved surface area.
Answer
Step 1: Find slant height using l² = r² + h² l² = 5² + 12² = 25 + 144 = 169 l = √169 = 13 cm Step 2: Find curved surface area CSA = πrl = (22/7) × 5 × 13 = (22 × 65)/7 = 1430/7 ≈ 204.29 cm² Answer: …
Find the total surface area of a cone with base radius 6 cm and slant height 10 cm.
Answer
Formula: Total Surface Area = πrl + πr² = πr(l + r) Step 1: Identify values → r = 6 cm, l = 10 cm Step 2: Apply formula → TSA = π × 6 × (10 + 6) = π × 6 × 16 Step 3: Calculate → TSA = (22/7) × 6 × 16 …
Find the surface area of a sphere with radius 14 cm.
Answer
Formula: Surface Area of Sphere = 4πr² Step 1: Identify given value → r = 14 cm Step 2: Apply formula → SA = 4π(14)² Step 3: Calculate → SA = 4 × (22/7) × 196 = 4 × 22 × 28 = 2464 cm² Answer: 2464 cm²…
A spherical ball has diameter 21 cm. Find its surface area.
Answer
Step 1: Find radius from diameter → r = 21/2 = 10.5 cm Step 2: Apply formula → SA = 4πr² Step 3: Calculate → SA = 4 × (22/7) × (10.5)² = 4 × (22/7) × 110.25 = (4 × 22 × 110.25)/7 = 9702/7 = 1386 cm² A…
Find the curved surface area of a hemisphere with radius 7 cm.
Answer
Formula: Curved Surface Area of Hemisphere = 2πr² Step 1: Identify given value → r = 7 cm Step 2: Apply formula → CSA = 2π(7)² Step 3: Calculate → CSA = 2 × (22/7) × 49 = 2 × 22 × 7 = 308 cm² Answer: …
Find the total surface area of a hemisphere with radius 10.5 cm.
Answer
Formula: Total Surface Area of Hemisphere = 3πr² Step 1: Identify given value → r = 10.5 cm Step 2: Apply formula → TSA = 3π(10.5)² Step 3: Calculate → TSA = 3 × (22/7) × 110.25 = (3 × 22 × 110.25)/7 …
Find the volume of a cone with base radius 6 cm and height 8 cm.
Answer
Formula: Volume of Cone = (1/3)πr²h Step 1: Identify values → r = 6 cm, h = 8 cm Step 2: Apply formula → V = (1/3) × π × 6² × 8 Step 3: Calculate → V = (1/3) × (22/7) × 36 × 8 = (22 × 36 × 8)/(3 × 7) …
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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