Question

the diameter of a sphere decreased by 25% by what percent does its total surface area decrease​

Answer 1

Let, the diameter of a sphere be 2r

Radius = diameter/2 = 2r/2 = r

As we know that :

Total surface area of Sphere = 4πr^2, where r = radius of the sphere

After decreasing by 25% the diameter of sphere = 2r×(100-25)/100 = 2r×75/100 = 6r/4 = 3r/2

Now, total surface area of sphere = 4π(3r/2/2)^2

=> TSA of Sphere = 4π(3r/4)^2 = 4×9πr^2/16 = 9πr^2/4

Decreasing in the percentage :

(4πr^2-9πr^2/4)/(4πr^2) × 100

=> 7πr^2/16πr^2 × 100 = 7×25/4 = 175/4 = 43.75%

So, the total surface area of sphere will be decreased by 43.75% ✔✔

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Hope it helps ☺

Fóllòw Më ❤