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13 Jan 2021, 09:00
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C
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Difficulty:
75%
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Question Stats:
48% (02:34) correct
52%
(02:27)
wrong
based on 27
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A cylindrical vessel is filled with water up to some height. If a sphere of diameter 8 cm is dropped into the cylinder, the water level rises by half of the initial level. Instead, if a sphere of diameter 16 cm is dropped, the water level rises to a height \(h_2\). What percentage of this new height \(h_2\) is the initial level of water?
A. \(16 \frac{1}{6}\)%
B. 20%
C. 25%
D. \(33\frac{1}{3}\)%
E. 40%
A. \(16 \frac{1}{6}\)%
B. 20%
C. 25%
D. \(33\frac{1}{3}\)%
E. 40%
13 Jan 2021, 10:05
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A cylindrical vessel is filled with water up to some height. If a sphere of diameter 8 cm is dropped into the cylinder, the water level rises by half of the initial level. Instead, if a sphere of diameter 16 cm is dropped, the water level rises to a height h2. What percentage of this new height h2 is the initial level of water?
1st case: Volume of water rise = volume of sphere dropped
or, Pie*r^2*h/2 = 4/3 * pie*4^3 or, r^2*h = 8/3 *4^3
2nd case: Volume of water rise = volume of sphere dropped
or, or, Pie*r^2*h2 = 4/3 * pie*8^3 or, r^2*h2 = 4/3 *8^3
So, r^2*h/r^2*h2 *100 = (8/3 *4^3)/(4/3 *8^3) *100 or, h/h2 = 1/4 *100 = 25%
I think C.
1st case: Volume of water rise = volume of sphere dropped
or, Pie*r^2*h/2 = 4/3 * pie*4^3 or, r^2*h = 8/3 *4^3
2nd case: Volume of water rise = volume of sphere dropped
or, or, Pie*r^2*h2 = 4/3 * pie*8^3 or, r^2*h2 = 4/3 *8^3
So, r^2*h/r^2*h2 *100 = (8/3 *4^3)/(4/3 *8^3) *100 or, h/h2 = 1/4 *100 = 25%
I think C.
19 Jan 2021, 09:31
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Bunuel
Volume of sphere = Volume of water displaced
When Sphere with Diameter 8 is put in then:
\(\frac{4}{3}\pi4^3\)=\( \pi(r^2)\frac{1}{2}h\) ...\((i)\)
Where\(\hspace{1mm} r= \)radius of the cylinder
\(h=\) initial height of water
When Sphere of Diameter 16 cms is dropped in :
\(\frac{4}{3}\pi8^3\)=\( \pi(r^2)h_2\)....\((ii)\)
Dividing \((i) \)by \((ii)\)
\(\frac{4*4*4}{8*8*8}=\frac{h}{2*h_2}\) So \(\frac{h}{h_2}=\frac{1}{4}\)
\(\frac{h}{h_2}*100= \frac{1}{4}*100 = 25 \%\)
Bunuel please look into this.
Ans- Should be C
