Mensuration — Flashcards
ICSE · Class 10 · Mathematics
28 flashcards for Mensuration (ICSE Class 10 Mathematics) to test yourself on key terms and facts. Sample: "Find the curved surface area of a cylinder"
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Get startedFind the curved surface area of a cylinder with radius 7 cm and height 10 cm.
Answer
Step 1: Use the formula for curved surface area of cylinder: 2 \pi r h. Step 2: Substitute r = 7 and h = 10. Step 3: CSA = 2 \pi × 7 × 10 = 140\pi. Answer: 140\pi cm². If \pi = 22/7, then CSA = 440 cm…
Find the total surface area of a cylinder with radius 5 cm and height 12 cm.
Answer
Step 1: Use the formula for total surface area of cylinder: 2 \pi r(h+r). Step 2: Substitute r = 5 and h = 12. Step 3: TSA = 2 \pi × 5 × (12+5) = 10\pi × 17 = 170\pi. Answer: 170\pi cm². If \pi = 22/7…
Find the volume of a cylinder with radius 3.5 cm and height 8 cm.
Answer
Step 1: Use the formula for volume of cylinder: \pi r²h. Step 2: Substitute r = 3.5 and h = 8. Step 3: V = \pi × (3.5)² × 8 = \pi × 12.25 × 8 = 98\pi. Answer: 98\pi cm³. If \pi = 22/7, then V = 308 cm…
A cylinder has radius 4 cm and height 9 cm. If its top and bottom are removed, what surface area remains?
Answer
Step 1: When top and bottom are removed, only curved surface area remains. Step 2: Use CSA of cylinder = 2 \pi r h. Step 3: Substitute r = 4 and h = 9. Step 4: CSA = 2 \pi × 4 × 9 = 72\pi. Answer: 72\…
A hollow cylinder has external radius 7 cm, internal radius 5 cm, and height 10 cm. Find the volume of material used.
Answer
Step 1: Use volume of material of hollow cylinder: \pi h(R²-r²). Step 2: Substitute R = 7, r = 5, h = 10. Step 3: V = \pi × 10 × (49-25) = 10\pi × 24 = 240\pi. Answer: 240\pi cm³. If \pi = 22/7, then …
A hollow cylinder has external radius 8 cm, internal radius 6 cm, and height 12 cm. Find its curved surface.
Answer
Step 1: Use curved surface of hollow cylinder: 2 \pi h(R+r). Step 2: Substitute R = 8, r = 6, h = 12. Step 3: CSA = 2 \pi × 12 × (8+6) = 24\pi × 14 = 336\pi. Answer: 336\pi cm². If \pi = 22/7, then CS…
A hollow cylinder has external radius 6 cm, internal radius 4 cm, and height 5 cm. Find its total surface area.
Answer
Step 1: Use total surface area of hollow cylinder: 2 \pi(R+r)(h+R-r). Step 2: Substitute R = 6, r = 4, h = 5. Step 3: TSA = 2 \pi(6+4)(5+6-4) = 2 \pi × 10 × 7 = 140\pi. Answer: 140\pi cm². If \pi = 22…
Why is the total surface area of a hollow cylinder not found by adding separate base areas again?
Answer
The formula already includes all exposed parts: the external curved surface, internal curved surface, and the two annular rings at the ends. So adding extra base areas again would count the same surfa…
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