4. "The Total Surface Area (TSA) of a sphere is 16piesq.units and the TSA of a hemisphere with same radius is 8 pi^ prime " Do you agree with this statement? Justify your answer with a reason.
Answers
Step-by-step explanation:
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Answer: No, I don't agree with this assertion. Assuming they have the same radius, the numbers for the total surface area (TSA) of a sphere and a hemisphere are incongruent.
Explanation:
A sphere's TSA is calculated using the formula 4r2, where r is the sphere's radius. When we enter TSA = 16 sq. units in its place, we get:
4πr^2 = 16π
When we simplify this equation, we obtain:
r^2 = 4
r = 2
The sphere's radius is thus 2 units.
The TSA of a hemisphere is now calculated using the formula 3r2, where r is the hemisphere's radius. When we replace the specified value of TSA = 8' units, we obtain:
3πr^2 = 8π'
When we simplify this equation, we obtain:
r^2 = 8/3
r = sqrt(8/3)
Hence the hemisphere's radius, which is sqrt(8/3) units, is not the same as the sphere's radius.
Because of this, we cannot assume that the radius of the sphere and the hemisphere is the same based on the TSA numbers that have been provided.
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