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# Circle B’s diameter was multiplied by 1.8. By what percent, approximat

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SVP
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Circle B’s diameter was multiplied by 1.8. By what percent, approximat [#permalink]

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18 Sep 2017, 13:07
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45% (medium)

Question Stats:

57% (01:22) correct 43% (01:18) wrong based on 23 sessions

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Circle B’s diameter was multiplied by 1.8. By what percent, approximately, was the area increased?
A 80%
B 125%
C 225%
D 325%
E 375%

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Intern
Joined: 16 Dec 2012
Posts: 3
Re: Circle B’s diameter was multiplied by 1.8. By what percent, approximat [#permalink]

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18 Sep 2017, 14:26
Correct Answer :- 225 % , Area = pi*r^2 , and as diameter is multiplied by 1.8 , Final Area would be 1.8^2 time Initial Area , i.e 3.24 A i Total increase in area :- 3.24 - 1 = 2.24 A , and thus % increase :- 225 %

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Circle B’s diameter was multiplied by 1.8. By what percent, approximat [#permalink]

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18 Sep 2017, 15:35
1
Circle B’s diameter was multiplied by 1.8. By what percent, approximately, was the area increased?
A 80%
B 125%
C 225%
D 325%
E 375%

Use $$k^2$$

Area, including for circles, equals length * length.

If given a length and a scale factor $$k$$, to find the percent increase in area from an increase in length, use $$k^2$$ (what happens to one length also happens to the other length).

Here: (1.8)(1.8) = 3.24

This scale factor includes the original 1. Percent increase is

$$\frac{New - Old}{Old}$$ * 100 =

$$\frac{3.24 - 1}{1}$$ * 100 = 224%

Choose values

You could test numbers and use fractions.

The diameter is multiplied by 1.8 = $$\frac{180}{100}$$ = $$\frac{18}{10}$$

So let D = 10

Original area? r = 5, area is $$25\pi$$

New area? New D = 18, r = 9, area is $$81\pi$$

Percent increase: $$\frac{81-25}{25}$$ = $$\frac{56}{25}$$ * 100 =

224 percent

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Circle B’s diameter was multiplied by 1.8. By what percent, approximat   [#permalink] 18 Sep 2017, 15:35
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