Question

The diameter of hemisphere is decreased by 30%. By what % it's CSA decreased ?

Answer 1

Let the diameter of hemisphere x

decrease in diameter of hemisphere = 30x/100

New diameter x - 30x/100 = 70x/100

old 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 %
Hope this helps you !!