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

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
The formula for the volume of a sphere is 43πr3. If the radius of a  [#permalink]

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21 Jan 2019, 22:57
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Difficulty:

15% (low)

Question Stats:

87% (00:41) correct 13% (02:17) wrong based on 39 sessions

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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

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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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22 Jan 2019, 03:08
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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22 Jan 2019, 13:23
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.

$$k^3=2^3=8$$

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?
$$\frac{\frac{256}{3}π}{\frac{32}{3}π}=(\frac{256}{3}π*\frac{3}{32}π)=8$$

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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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22 Jan 2019, 19:25
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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Joined: 16 Dec 2018
Posts: 10
Re: The formula for the volume of a sphere is 43πr3. If the radius of a  [#permalink]

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22 Jan 2019, 21:39
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, 21:39
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