If the radius of a circle is increased by 50%, what will be the percentage increase in its area?

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Area and Perimeter

1. Area of a triangle =12×Base ×height

2. Area of a triangle

=ss-as-b(s-c), where

s=a+b+c2

3. Area of an equilateral triangle

=34×Side2

4. Area of a circle =πr2

5. Circumference of a circle =2πr

6. Area of a sector of a circle =360°×πr2

7. Area of a square =Side2

8. Perimeter of a square =4×Side

9. Perimeter of a Rectangle

=2(length+breadth)

Area of a Rectangle = (length+breadth)

10. A rhombus is a parallelogram that has all the sides equal. In a rhombus, diagonals always bisect each other.

Area =12×d1×d2

11. A quadrilateral whose opposite sides are parallel is called a parallelogram. Diagonals of a parallelogram bisect each other. Area =Base ×Height

12. A trapezium is a quadrilateral with only two sides parallel to each other. Area =12 Sum of parallel sides × Height

In geometry, the straight lines which do not meet are called parallel. A line that crosses a pair of parallel lines is known as transversal. Watch and learn...

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If the diameter of a circle increases by 50 percent, by what percent [#permalink]

10 Jan 2019, 02:27

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If the diameter of a circle increases by 50 percent, by what percent will the area of the circle increase?A. 25%B. 50%C. 100%D. 125%

E. 225%

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Re: If the diameter of a circle increases by 50 percent, by what percent [#permalink]

10 Jan 2019, 02:57

My answer DIf the diameter increases 50%, the radius also increases 50%.The area would remain Pi(r^2)Say for example Radius increases from 10 to 15the area would increase from 100pi to 225pi.

therefore 125% increase.

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Re: If the diameter of a circle increases by 50 percent, by what percent [#permalink]

10 Jan 2019, 05:06

Bunuel wrote:

If the diameter of a circle increases by 50 percent, by what percent will the area of the circle increase?A. 25%B. 50%C. 100%D. 125%

E. 225%

radius = 2 dia 4area = 4pi50% increase in dia = 4*1.5 = 6radius = 3area = 9pi

% change in area = 9pi-4Pi/ 4 pi = 125 % IMO D

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If the diameter of a circle increases by 50 percent, by what percent [#permalink]

10 Jan 2019, 06:32

Solution

Given:

• The diameter of a circle increases by 50%
To find:

• The percentage increase in area of the circle
Approach and Working: Let ‘d‘ be the initial diameter

• Area = \(ᴨ\frac{d^2}{4}\) = ANew diameter = \(d + \frac{d}{2} = \frac{3d}{2}\)

• Area = \(ᴨ(\frac{3d}{2})^2/4 = 9ᴨ\frac{d^2}{16} = \frac{9A}{4}\)Percentage increase in area = \([(\frac{9A}{4} – A)/A] *100 = 125\)%Hence, the correct answer is Option D

Answer: D

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Re: If the diameter of a circle increases by 50 percent, by what percent [#permalink]

20 Jun 2020, 14:30

Bunuel wrote:

If the diameter of a circle increases by 50 percent, by what percent will the area of the circle increase?A. 25%B. 50%C. 100%D. 125%

E. 225%

Solution:

If the diameter of a circle increases by 50 percent, the radius also increases by 50 percent. If we let the original radius = 10, the new radius = 15. Thus, we have:Area of the original circle = 10^2 x π = 100π Area of the new circle = 15^2 x π = 225π We use the percent change formula: (New - Old) / Old x 100. Therefore, the area of the circle increases by(225π - 100π)/(100π) x 100 = 125π/π = 125 percent

Answer: D

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Re: If the diameter of a circle increases by 50 percent, by what percent [#permalink]

20 Jun 2020, 14:30