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The formula for the volume of a sphere is 43πr3. If the radius of a

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The formula for the volume of a sphere is 43πr3. If the radius of a  [#permalink]

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New post 21 Jan 2019, 23:57
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

89% (00:45) correct 11% (02:17) wrong based on 44 sessions

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Re: The formula for the volume of a sphere is 43πr3. If the radius of a  [#permalink]

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New post 22 Jan 2019, 04:08
Bunuel wrote:
The formula for the volume of a sphere is \(\frac{4}{3}πr^3\). If the radius of a sphere is doubled, the volume of the resulting sphere will be how many times the volume of the original sphere?


A 2
B 4
C 8
D 16
E 32



let original r = 1
and double = r = 2
so original * x = new
4/3 * pi * 1 * x = 32* pi /3

x = 8
IMO C
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The formula for the volume of a sphere is 43πr3. If the radius of a  [#permalink]

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New post 22 Jan 2019, 14:23
Bunuel wrote:
The formula for the volume of a sphere is \(\frac{4}{3}πr^3\). If the radius of a sphere is doubled, the volume of the resulting sphere will be how many times the volume of the original sphere?


A 2
B 4
C 8
D 16
E 32

Scale Factor
When the volume of figures increases or decreases, each length is multiplied by a scale factor.

Volume = length * length * length

Each length is doubled. Scale factor is 2.

Scale factor \(k = 2\)

Multiply the original figure by scale factor, cubed, to calculate change, because
the scale factor changes all three lengths.

\(k^3=2^3=8\)

Answer C

Plug in values

If the original radius is 2, and the radius is doubled, then the new radius is 4.
Original volume?
\(\frac{4}{3}πr^3\)
\(\frac{4}{3}π2^3=\)
\(\frac{32}{3}π\)

New volume?
\(\frac{4}{3}πr^3\)
\(\frac{4}{3}π4^3\)
\(\frac{256}{3}π\)

Volume of new sphere is how many times bigger than original sphere?
\(\frac{\frac{256}{3}π}{\frac{32}{3}π}=(\frac{256}{3}π*\frac{3}{32}π)=8\)

Answer C
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Re: The formula for the volume of a sphere is 43πr3. If the radius of a  [#permalink]

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New post 22 Jan 2019, 20:25
Given r=2 so cube of r will be 8. Rest everything will remain same.


Therefore volume will be 8 times the original.

IMO C.
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Re: The formula for the volume of a sphere is 43πr3. If the radius of a  [#permalink]

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New post 22 Jan 2019, 22:39
4/3pie (8r^3)

Which is 8times the orginal. So ans is C

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Re: The formula for the volume of a sphere is 43πr3. If the radius of a   [#permalink] 22 Jan 2019, 22:39
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