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10 Nov 2020, 02:00
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C
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Difficulty:
25%
(medium)
Question Stats:
79% (01:44) correct
21%
(01:33)
wrong
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A cylindrical silo and a rectangular silo are both being filled with 400 m^3 of corn. The cylindrical silo has a base with an area of 20 m^2. The rectangular silo has a base with an area of 10 m^2. Assuming that the corn will not overflow in either, which statement will be true about the corn levels?
A. The cylindrical silo level will be 20 m higher.
B. The cylindrical silo level will be 10 m lower.
C. The rectangular silo level will be 20 m higher.
D. The rectangular silo level will be 40 m higher.
E. The rectangular silo level will be the same as the cylindrical silo.
A. The cylindrical silo level will be 20 m higher.
B. The cylindrical silo level will be 10 m lower.
C. The rectangular silo level will be 20 m higher.
D. The rectangular silo level will be 40 m higher.
E. The rectangular silo level will be the same as the cylindrical silo.
12 Nov 2020, 08:40
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Bunuel
Volume of Cylindrical silo= \(\pi r^2 h\)
So \(\pi r^2 h=400\)
\(20*h=400\)
\(h=20\)
Volume of rectangular silo l*b*h
Hence \(l*b*h = 400\)
\(10*h=400\)
\(h=40\)
So we can see corn in rectangular silo is \(20\hspace{1mm} m \) higher than height of corn in cylindrical silo.
Ans-C
Hope it's clear.
12 Nov 2020, 09:30
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Bunuel
Both shapes have a flat base/lid, and each horizontal slice of their shape has the same area so we can use the simple relation: \(Volume = Area of Base * Height\) for both shapes. Thus the height of the cylinder is 400/20 = 20, the height of the rectangular prism is 400/10 = 40. Therefore the rectangular prism is 20 m higher.
Ans: C
