the daimeter of a hemisphere is decrease by 30%.what will be the percentage change in its total surface area?
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≡QUESTION≡
The diameter of a hemisphere is decreased by 30%. What will be the percentage change in its total surface area?
║⊕ANSWER⊕║
Let the diameter of hemisphere be x
Decrease in diameter of hemisphere = 30x/100
New diameter = x - 30x/100
= 70x/100
Original TSA = 3πr² = 3π × (x/2)²
New TSA = 3π x (70x/200)²
Let the percent change be R
R % of (x/2)² = (70x/200)²
( R/100) x (x²/4) = 4900 x² / 40000
R/400 = 4900/40000
R = 4900/100
R = 49 %
∴The % change in its total surface area is 49%.
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