Question

the diameter of hemisphere is decreased by 30%What will be the %change in its T.S.A?

Answer 1

The radius = diameter /2 = d/2
If decreased by 30%
Then diameter = 30%of d
Therefore radius = 30%of r
T. S. A= 3pier2
And if decreased = 3pie30%r²
= 3pie900%r= 900%(3pier²)
Therefore 900 %is decreased
Bye

Answer 2

We know that,
T. S. A of hemisphere = 2πr²

T. S. A = 2π (d²)/4 = πd²/2 .

Diameter is decreased by 30% : d - 3/10d = 7/10d .

New T. S. A
= π ( 7/10d²)/2
= π(49/100)d² / 2
= πd² ( 49/100) * 1/2
= πd² ( 49/200)

Change in T. S. A
= πd²/2 ( 49/100 - 1 )
= πd²/2 ( 49 - 100/ 100 )
= πd²/2 ( -51/100)

% increase in T.S.A = -51/100 * 100% = 51% .

Hope helped!

Therefore, There is a 51% decrease in hemisphere area