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605-655 Level|   Geometry|      
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If a solid spherical ball of iron with radius r centimetres 05 Jan 2018, 10:38
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45% (medium)

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55% (01:31) correct 45% (01:20) wrong based on 67 sessions

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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
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A
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If a solid spherical ball of iron with radius r centimetres 05 Jan 2018, 11:35
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mandeey
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
Careful here - don't forget the surface area of the circular flat base of the hemisphere

Volume of a sphere:
\(\frac{4}{3} \pi r^3\)
Volume of a hemisphere is half of that:
\(\frac{4}{3} \pi r^3 * \frac{1}{2}\\
=\frac{2}{3} \pi r^3\)

Surface area of a sphere:\(4\pi r^2\)

Surface area of hemisphere =
\(\frac{1}{2}\) the round part of sphere + surface area of circular base

Half of the round part of the sphere's SA = \(2\pi r^2\)
The hemisphere's circular base SA = \(\pi r^2\)
Add them. \(2\pi r^2 + \pi r ^2 = 3\pi r^2\)

Ratio of hemisphere's volume to hemisphere's SA:

\(\frac{\frac{2}{3} \pi r^3}{3\pi r^2}\\
= \frac{2r}{9}\)

Answer A

Not sure this question is sub-600. SA of a hemisphere with no formula given? :-)
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If a solid spherical ball of iron with radius r centimetres 16 Apr 2022, 12:14
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