Surface Areas and Volumes - Flash Cards
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What is the formula for the total surface area (TSA) of a cylinder?
TSA of a cylinder = 2πr(h + r), where r is the radius and h is the height.
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How do you calculate the curved surface area (CSA) of a cone?
CSA of a cone = πrl, where r is the base radius and l is the slant height.
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What is the formula for the volume of a cylinder?
Volume = πr²h, where r is the radius and h is the height.
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What is the formula for the surface area of a sphere?
Surface Area = 4πr², where r is the radius of the sphere.
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What is the volume formula for a cone?
Volume = (1/3)πr²h, where r is the base radius and h is the height.
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What is the total surface area of a hemisphere?
Total Surface Area = 3πr², where r is the radius.
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What is the difference between Total Surface Area and Curved Surface Area?
TSA includes all surfaces, while CSA only includes the curved part, excluding bases.
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What is the formula for the volume of a sphere?
Volume = (4/3)πr³, where r is the radius.
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How do you find the TSA of combined solids?
Break into individual solids, calculate TSA for each, and sum the appropriate areas while excluding shared surfaces.
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How do you find the CSA of a cylinder?
CSA = 2πrh, where r is the radius and h is the height.
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What is the TSA of a cone surmounted by a hemisphere?
TSA = CSA of cone + CSA of hemisphere; TSA = πrl + 2πr².
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How do you determine the height of a composite solid?
Subtract the heights of the top solid parts from the total height of the composite.
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What is a common mistake in calculating TSA?
Not considering the area of shared surfaces between combined solids.
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When do you use the formula for the TSA of a solid?
Use it to find the area that needs coverage, such as painting or wrapping.
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Calculate TSA of a block made of a cube (5 cm edge) and a hemisphere (4.2 cm diameter).
TSA = 150 + πr² (2) = 156.92 cm² (approx).
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What unit is used for measuring volume?
Volume is typically measured in cubic units, e.g., cm³ or m³.
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How to find area to be painted on a composite solid?
Calculate CSA for exposed surfaces and exclude bases where two solids are joined.
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What is the CSA of a hemisphere?
CSA = 2πr², where r is the radius.
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Where do we see solids in real life?
Examples include containers, buildings, and toys shaped as cones, cylinders, and spheres.
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