Surface Areas and Volumes
Uttar Pradesh Board · Class 10 · Mathematics
Flashcards for Surface Areas and Volumes — Uttar Pradesh Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedWhat are the basic solids that we combine to form composite solids?
Answer
The basic solids are: Cuboid, Cone, Cylinder, Sphere, and Hemisphere. These can be combined in various ways to create composite shapes like containers, toys, and monuments.
What does TSA and CSA stand for in the context of surface areas?
Answer
TSA = Total Surface Area (includes all surfaces of a solid) CSA = Curved Surface Area (includes only the curved surfaces, excluding flat bases)…
How do we find the total surface area of a composite solid?
Answer
For composite solids, TSA = Sum of curved surface areas of individual components. We don't include the surfaces that are joined together (hidden surfaces). Example: For cylinder with hemispheres at en…
A container is made of a cylinder with hemispheres at both ends. Write the formula for its total surface area.
Answer
TSA = CSA of cylinder + CSA of 2 hemispheres TSA = 2πrh + 2 × 2πr² TSA = 2πrh + 4πr² TSA = 2πr(h + 2r) where r = radius and h = height of cylindrical part…
What is the TSA of a toy made by joining a cone and a hemisphere at their bases?
Answer
TSA = CSA of cone + CSA of hemisphere TSA = πrl + 2πr² where r = common radius of base, l = slant height of cone Note: The flat circular bases are not included as they are joined together.
Find the TSA of a solid consisting of a cylinder surmounted by a cone, both having radius 7 cm. Height of cylinder = 10 cm, height of cone = 6 cm.
Answer
Given: r = 7 cm, h₁ = 10 cm (cylinder), h₂ = 6 cm (cone) Slant height of cone, l = √(r² + h₂²) = √(49 + 36) = √85 cm TSA = CSA of cylinder + CSA of cone + Area of base TSA = 2πrh₁ + πrl + πr² TSA = 2π…
How do we calculate the volume of composite solids?
Answer
Volume of composite solid = Sum of volumes of individual components Unlike surface area, we simply add all the volumes because no volume is lost when joining solids. Example: Volume of cylinder with h…
Write the volume formula for a container made of a cylinder with hemispheres at both ends.
Answer
Volume = Volume of cylinder + Volume of 2 hemispheres Volume = πr²h + 2 × (2/3)πr³ Volume = πr²h + (4/3)πr³ Volume = πr²(h + 4r/3) where r = radius and h = height of cylindrical part…
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