Skip to main content
Super TutorResources
Chapter 10 of 14
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Flashcards

Surface Areas and Volumes

Karnataka Board · Class 10 · Mathematics

Flashcards for Surface Areas and Volumes — Karnataka Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.

45 questions20 flashcards4 concepts

Interactive on Super Tutor

Studying Surface Areas and Volumes? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for flashcards and more.

Try Super Tutor — Free

1,000+ Class 10 students started this chapter today

20 Flashcards
Card 1Surface Area of Combination of Solids

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 …

Card 2Volume of Combination of Solids

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…

Card 3Surface Area Concepts

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…

Card 4Surface Area of Combination of Solids

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…

Card 5Formulas and Applications

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…

Card 6Surface Area of Combination of Solids

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 …

Card 7Volume of Combination of Solids

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.

Card 8Volume of Combination of Solids

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…

+12 more flashcards available

Practice All

Frequently Asked Questions

What are the important topics in Surface Areas and Volumes for Karnataka Board Class 10 Mathematics?
Surface Areas and Volumes covers several key topics that are frequently asked in Karnataka Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Surface Areas and Volumes — Karnataka Board Class 10 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.
How many flashcards are available for Surface Areas and Volumes?
There are 20 flashcards for Surface Areas and Volumes covering key definitions, formulas, and concepts. Use them daily for 10–15 minutes for best results.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Surface Areas and Volumes

All 14 chapters — Karnataka Board Class 10 Mathematics Flashcards

For serious students

Get the full Surface Areas and Volumes chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for Karnataka Board Class 10 Mathematics.

Try Super Tutor Free
Try the full chapter — Free