Surface areas and Volumes — Important Questions
Telangana Board · Class 9 · Mathematics
45 important questions from Surface areas and Volumes for Telangana Board Class 9 Mathematics, with answers. Includes multiple choice questions.
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Important Questions from Surface areas and Volumes
Find the volume of a cylinder with base radius 4 cm and height 9 cm. (Take π = 22/7)
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1584/7 cm³
Step 1: Given radius (r) = 4 cm, height (h) = 9 cm, π = 22/7. Step 2: Apply volume formula V = πr²h. Step 3: Substitute values: V = (22/7) × 4² × 9. Step 4: Calculate: V = (22/7) × 16 × 9 = (22 × 144)/7. Step 5: Simplify: V = 3168/7 = 1584/7 cm³. This equals approximately 226.3 cm³.
A cone has base radius 6 cm and height 8 cm. What is its slant height?
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10 cm
Step 1: Given radius (r) = 6 cm and height (h) = 8 cm. Step 2: Use the relationship l² = h² + r² where l is slant height. Step 3: Substitute values: l² = 8² + 6² = 64 + 36 = 100. Step 4: Take square root: l = √100 = 10 cm. Step 5: Verify using Pythagorean theorem - this forms a 6-8-10 right triangle, which is a multiple of the 3-4-5 triangle.
Find the curved surface area of a cone with radius 7 cm and slant height 15 cm. (Take π = 22/7)
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330 cm²
Step 1: Given radius (r) = 7 cm, slant height (l) = 15 cm, π = 22/7. Step 2: Apply curved surface area formula CSA = πrl. Step 3: Substitute values: CSA = (22/7) × 7 × 15. Step 4: Simplify: The 7s cancel out, so CSA = 22 × 15 = 330 cm². Step 5: This represents the area of the sector that would form the cone when unfolded.
What is the volume of a cone with base radius 5 cm and height 12 cm? (Take π = 22/7)
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1100/7 cm³
Step 1: Given radius (r) = 5 cm, height (h) = 12 cm, π = 22/7. Step 2: Apply volume formula V = (1/3)πr²h. Step 3: Substitute values: V = (1/3) × (22/7) × 5² × 12. Step 4: Calculate: V = (1/3) × (22/7) × 25 × 12 = (22 × 300)/(7 × 3). Step 5: Simplify: V = 6600/21 = 1100/7 cm³, which equals approximately 157.14 cm³.
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