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A cylindrical tank has a height of 10 feet and a base with a radius of
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14 May 2021, 00:14
14 May 2021, 00:14
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A cylindrical tank has a height of 10 feet and a base with a radius of 6 feet. If the thickness of the tank’s sides is negligible, what is the volume, in cubic feet, of the largest rectangular solid that could be placed inside the tank?
A. 60
B. 360
C. \(240\sqrt{3}\)
D. \(360\sqrt{2}\)
E. 720
A. 60
B. 360
C. \(240\sqrt{3}\)
D. \(360\sqrt{2}\)
E. 720
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
A cylindrical tank has a height of 10 feet and a base with a radius of
[#permalink]
15 May 2021, 23:33
15 May 2021, 23:33
Explanation:
The largest rectangular solid that could be placed inside the tank is one with all the vertices on the curved surface of the tank
i.e. Diameter of the circular base = Diagonal of the rectangular face
\(12 = \sqrt{l^2 + b^2}\)
Also, the volume would be maximum when the solid is square faced with height equal to that of cylindrical tank.
Therefore, \(l = b = a\)
i.e. \(12 = \sqrt{a^2 + a^2}\)
\(a = \frac{12}{\sqrt{2}}\)
Now, the volume = \(a^2H = (\frac{12}{\sqrt{2}})^2(10) = 720\)
Hence, option E
The largest rectangular solid that could be placed inside the tank is one with all the vertices on the curved surface of the tank
i.e. Diameter of the circular base = Diagonal of the rectangular face
\(12 = \sqrt{l^2 + b^2}\)
Also, the volume would be maximum when the solid is square faced with height equal to that of cylindrical tank.
Therefore, \(l = b = a\)
i.e. \(12 = \sqrt{a^2 + a^2}\)
\(a = \frac{12}{\sqrt{2}}\)
Now, the volume = \(a^2H = (\frac{12}{\sqrt{2}})^2(10) = 720\)
Hence, option E
gmatclubot
A cylindrical tank has a height of 10 feet and a base with a radius of [#permalink]
15 May 2021, 23:33
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