Surface Areas and Volumes — Flashcards
Gujarat Board · Class 10 · Mathematics
20 flashcards for Surface Areas and Volumes (Gujarat Board Class 10 Mathematics) to test yourself on key terms and facts.
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What are the four basic solids that we commonly combine to form complex shapes?
Answer
The four basic solids are: 1. Cuboid 2. Cone 3. Cylinder 4. Sphere (including hemisphere) These shapes can be combined in various ways to create complex objects like containers, toys, monuments, and …
Give three real-life examples of combination solids that we see in daily life.
Answer
Common examples include: 1. **Truck container**: A cylinder with hemispheres at both ends 2. **Test tube**: A cylinder with a hemisphere at one end 3. **Ice cream cone**: A cone with a hemisphere on t…
What is the key principle for finding the surface area of a combination solid?
Answer
**Key Principle**: The total surface area of a combination solid equals the sum of the curved surface areas of the individual components, MINUS the areas of the surfaces that are joined together. For…
A solid is formed by joining a hemisphere to the top of a cylinder. Write the formula for its total surface area.
Answer
For a cylinder topped with a hemisphere: **TSA = CSA of cylinder + CSA of hemisphere + Base area of cylinder** TSA = 2πrh + 2πr² + πr² TSA = 2πrh + 3πr² Where: - r = radius of both cylinder and hem…
What is the formula for the total surface area of a capsule (two hemispheres joined together)?
Answer
For a capsule (two hemispheres joined): **TSA = CSA of first hemisphere + CSA of second hemisphere** TSA = 2πr² + 2πr² **TSA = 4πr²** This is the same as the surface area of a complete sphere! Wher…
A cone is placed on top of a hemisphere. Write the formula for the total surface area.
Answer
For a hemisphere topped with a cone: **TSA = CSA of hemisphere + CSA of cone** TSA = 2πr² + πrl Where: - r = radius of both hemisphere and cone base - l = slant height of cone Note: The circular ba…
What does TSA and CSA stand for? Why do we use CSA when calculating surface areas of combination solids?
Answer
**TSA = Total Surface Area** (all surfaces of a solid) **CSA = Curved Surface Area** (only curved surfaces, excluding flat bases/tops) We use CSA for combination solids because: 1. Flat surfaces wher…
A solid consists of a cylinder with hemispherical ends. If radius = 7 cm and cylindrical height = 10 cm, find the total surface area.
Answer
Given: r = 7 cm, h = 10 cm **Solution:** TSA = CSA of cylinder + CSA of two hemispheres TSA = 2πrh + 2πr² + 2πr² TSA = 2πrh + 4πr² TSA = 2π(7)(10) + 4π(7)² TSA = 140π + 196π TSA = 336π **TSA = 336π c…
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