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What is the percentage increase in the volume of a sphere if it's radi

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Bunuel
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What is the percentage increase in the volume of a sphere if it's radi [#permalink] New post   29 Sep 2021, 04:15
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What is the percentage increase in the volume of a sphere if it's radius is increased by 3 times?

A. 1500
B. 1600
C. 2500
D. 2600
E. 2700
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D
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Capakki
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What is the percentage increase in the volume of a sphere if it's radi [#permalink] New post   Updated on: 05 Oct 2021, 09:00
No need to recall the formula:

Volume contains cube of radius i.e. r^3
If new radius is 3r then (3r)^3 will be 27 time of r^3
Difference 27r^3-r^3=26r^3
%change= Change / Original= [{(26r^3)/r^3}x100]=2600
Answer is D

Formula for Volume of sphere= 4/3*pi*r^3

Originally posted by Capakki on 29 Sep 2021, 09:48.
Last edited by Capakki on 05 Oct 2021, 09:00, edited 1 time in total.
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WheatyPie
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Re: What is the percentage increase in the volume of a sphere if it's radi [#permalink] New post   03 Oct 2021, 10:50
Capakki wrote:
No need to recall the formula:

Volume contains cube of radius i.e. r^3
If new radius is 3r then (3r)^3 will be 27 time of r^3
Difference 27r^3-r^3=26r^3
%change= Change / Original= [{(26r^3)/r^3}x100]=2600
Answer is C

Formula for Volume of sphere= 4/3*pi*r^3


Good solution, but 2600 is answer D.
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Capakki
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Re: What is the percentage increase in the volume of a sphere if it's radi [#permalink] New post   05 Oct 2021, 09:01
WheatyPie wrote:
Capakki wrote:
No need to recall the formula:

Volume contains cube of radius i.e. r^3
If new radius is 3r then (3r)^3 will be 27 time of r^3
Difference 27r^3-r^3=26r^3
%change= Change / Original= [{(26r^3)/r^3}x100]=2600
Answer is C

Formula for Volume of sphere= 4/3*pi*r^3


Good solution, but 2600 is answer D.


Updated. thank you
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ShaikhMoice
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Re: What is the percentage increase in the volume of a sphere if it's radi [#permalink] New post   29 Nov 2021, 12:49
Bunuel wrote:
What is the percentage increase in the volume of a sphere if it's radius is increased by 3 times?

A. 1500
B. 1600
C. 2500
D. 2600
E. 2700


Just 1 query,
if the existing radius is r and the same is increased by 3 times , isnt that means new radius is 4r.
Hence change in volume is 64-1=6300
kindly help with the doubt.
TIA
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JerryAtDreamScore
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Re: What is the percentage increase in the volume of a sphere if it's radi [#permalink] New post   29 Nov 2021, 14:29
Bunuel wrote:
What is the percentage increase in the volume of a sphere if it's radius is increased by 3 times?

A. 1500
B. 1600
C. 2500
D. 2600
E. 2700


Breaking Down the Info:

The formula of the volume of a sphere is \(V = \frac{4}{3}\pi r^3\).

From this formula, we would like to see V is proportional to the cube of \(r\).

If r is increased by 3 times, which is r is multiplied by 3, then \(r^3\) would be multiplied by \(3^3 = 27\). Therefore the volume is also multiplied by 27.

Note this is a 26x increase, hence 2600% percent increase. (I also don't like the original wording of the question; increased by 3 times sounds like the result is 4r for me).

Answer: D
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Re: What is the percentage increase in the volume of a sphere if it's radi [#permalink] New post   30 Nov 2021, 02:06
ShaikhMoice wrote:
Bunuel wrote:
What is the percentage increase in the volume of a sphere if it's radius is increased by 3 times?

A. 1500
B. 1600
C. 2500
D. 2600
E. 2700


Just 1 query,
if the existing radius is r and the same is increased by 3 times , isnt that means new radius is 4r.
Hence change in volume is 64-1=6300
kindly help with the doubt.
TIA


This is a good point.

300% of r => 3r
300% increase from r => 4r

Three times r => 3r
Three times increase from r => 4r
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Re: What is the percentage increase in the volume of a sphere if it's radi [#permalink]
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