By how much percent area is decreased if the radius of a circle is dec

1.	By how much percent area is decreased if the radius of a circle is decreased by 30%?
Answer» Let the radius of the circle is r. Therefore, the area of the circle is \(\pi\)r². After decreasing 30% radius of the circle, The actual radius of the circle is r – \(\frac{30}{100}r\) = r – 0.3r = 0.7 r. The area of the circle after decreasing = \(\pi\)(0.7r)² = 0.49 \(\pi r\) ². Decreased area = Area of circle before decreasing – Area of circle after decreasing = \(\pi r\)² – 0.49\(\pi r\)² = 0.51 \(\pi r\)² = 51% × Area of circle before decreasing. Hence, 51% area is decreased if the radius of a circle is decreased by 30%

By how much percent area is decreased if the radius of a circle is decreased by 30%?

Answer»

Let the radius of the circle is r.

Therefore, the area of the circle is \(\pi\)r².

After decreasing 30% radius of the circle,

The actual radius of the circle is r – \(\frac{30}{100}r\) = r – 0.3r = 0.7 r.

The area of the circle after decreasing = \(\pi\)(0.7r)² = 0.49 \(\pi r\) ².

Decreased area = Area of circle before decreasing – Area of circle after decreasing

= \(\pi r\)² – 0.49\(\pi r\)² = 0.51 \(\pi r\)²

= 51% × Area of circle before decreasing.

Hence, 51% area is decreased if the radius of a circle is decreased by 30%

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