Surface Areas and Volumes — Flashcards
Karnataka Board · Class 10 · Mathematics
20 flashcards for Surface Areas and Volumes (Karnataka Board Class 10 Mathematics) to test yourself on key terms and facts.
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A hemisphere is placed on top of a cylinder. The radius is 3.5 cm and cylinder height is 10 cm. Find the total surface area. (Use π = 22/7)
Answer
Step 1: Identify surfaces to include - CSA of hemisphere + CSA of cylinder + base area of cylinder. Step 2: CSA of hemisphere = 2πr² = 2 × (22/7) × (3.5)² = 77 cm². Step 3: CSA of cylinder = 2πrh = 2 …
A cone of height 4 cm is mounted on a hemisphere of radius 3 cm. Find the volume of the solid. (Use π = 22/7)
Answer
Step 1: Volume = Volume of hemisphere + Volume of cone. Step 2: Volume of hemisphere = (2/3)πr³ = (2/3) × (22/7) × 3³ = (2/3) × (22/7) × 27 = 198/7 cm³. Step 3: Volume of cone = (1/3)πr²h = (1/3) × (2…
When finding surface area of a combination of solids, why don't we add the complete surface areas of individual solids?
Answer
Because when two solids are joined, the surfaces at the junction are no longer exposed to the outside. Example: When a hemisphere sits on a cylinder, the circular base of hemisphere and top circular f…
A solid toy consists of a hemisphere surmounted by a cone. If radius is 2 cm and cone height is 3 cm, find slant height of cone and total surface area. (Use π = 3.14)
Answer
Step 1: Find slant height using l = √(r² + h²) = √(2² + 3²) = √(4 + 9) = √13 ≈ 3.6 cm. Step 2: Surface area = CSA of hemisphere + CSA of cone. Step 3: CSA of hemisphere = 2πr² = 2 × 3.14 × 4 = 25.12 c…
Formula for Curved Surface Area of hemisphere and when to use it
Answer
Formula: CSA = 2πr² (where r is radius). Use when: Finding surface area of hemisphere in combinations (like hemisphere on cylinder). Note: Total surface area of hemisphere = 3πr² (includes flat circul…
A medicine capsule is cylindrical with hemispherical ends. Total length 14 mm, diameter 5 mm. Find surface area. (Use π = 22/7)
Answer
Step 1: Radius = 2.5 mm, cylinder length = 14 - 5 = 9 mm. Step 2: Surface area = CSA of cylinder + CSA of 2 hemispheres. Step 3: CSA of cylinder = 2πrh = 2 × (22/7) × 2.5 × 9 = 990/7 mm². Step 4: CSA …
Find volume of air in a shed: cuboid base 7m × 15m × 8m with half-cylinder on top (diameter 7m). (Use π = 22/7)
Answer
Step 1: Volume = Volume of cuboid + Volume of half-cylinder. Step 2: Volume of cuboid = l × b × h = 15 × 7 × 8 = 840 m³. Step 3: Volume of half-cylinder = (1/2) × πr²h = (1/2) × (22/7) × (3.5)² × 15.
A glass has cylindrical shape with hemispherical depression at bottom. Inner diameter 5 cm, height 10 cm. Find actual capacity. (Use π = 3.14)
Answer
Step 1: Apparent capacity = πr²h = 3.14 × (2.5)² × 10 = 196.25 cm³. Step 2: Volume of hemisphere = (2/3)πr³ = (2/3) × 3.14 × (2.5)³ = 32.71 cm³. Step 3: Actual capacity = Apparent capacity - Volume of…
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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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