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# If a solid spherical ball of iron with radius r

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Intern
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If a solid spherical ball of iron with radius r [#permalink]  08 Jun 2019, 05:16
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If a solid spherical ball of iron with radius r centimetres is cut into two equal hemispheres, what is the ratio, in terms of r, of the volume and the surface area of each hemisphere?

A) 2r/9
B) r/3
C) 4r/9
D) 2r/3
E) 4r/3
[Reveal] Spoiler: OA
Manager
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Re: If a solid spherical ball of iron with radius r [#permalink]  14 Jun 2019, 08:25
V = 4/3* Pi*r^3, for half, V(1/2)= 2/3*Pi*r^3
A= 4*Pi*r^2 , for half, A(1/2)= 2*Pi*r^2 . but in this case, you also need to consider the area of a circular region (cutting sphere in middle!). So total surface area for half of the sphere, A(1/2)= 2*Pi*r^2 =Pi*r^2 = 3 *Pi*r^2

Now, V(1/2) / A(1/2) = 2*r/9
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Re: If a solid spherical ball of iron with radius r [#permalink]  15 Jun 2019, 08:17
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Expert's post
Please note that students are not required to know the formula for the volume of a sphere.
If you were given such a question on test day, the question would also include the formula for the volume of a sphere.

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: If a solid spherical ball of iron with radius r   [#permalink] 15 Jun 2019, 08:17
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