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Emily must ship a cylinder-shaped gift with a height of 11 inches and
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05 Dec 2022, 02:20
05 Dec 2022, 02:20
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71% (02:18) correct
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Emily must ship a cylinder-shaped gift with a height of 11 inches and a volume of 176π cubic inches. What is the volume, in cubic inches, of the smallest rectangular box which can contain this cylinder?
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704
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Emily must ship a cylinder-shaped gift with a height of 11 inches and
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07 Dec 2022, 11:14
07 Dec 2022, 11:14
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Carcass wrote:
Emily must ship a cylinder-shaped gift with a height of 11 inches and a volume of 176π cubic inches. What is the volume, in cubic inches, of the smallest rectangular box which can contain this cylinder?
Show: ::
704
Volume = \(πr^2H = 176π\)
\(r^2 = 16\)
\(r = 4\)
i.e. Diameter = \(8\)
So, dimensions of box has to be Height x Diameter x Diameter
Hence, the required volume = \((11)(8)(8) = 704\)
Re: Emily must ship a cylinder-shaped gift with a height of 11 inches and
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09 Dec 2022, 04:15
09 Dec 2022, 04:15
Expert Reply
OE
Because the cylinder’s height is 11 and its volume is 176π, and V = πr^2h, 176π = π(r^2)(11), and r = 4. The diameter of the cylinder is 8. The box will need a length of 8 and a width of 8 to accommodate the base of the cylinder, and a height of 11. The volume of the smallest box will equal 8 × 8 × 11, or 704.
Because the cylinder’s height is 11 and its volume is 176π, and V = πr^2h, 176π = π(r^2)(11), and r = 4. The diameter of the cylinder is 8. The box will need a length of 8 and a width of 8 to accommodate the base of the cylinder, and a height of 11. The volume of the smallest box will equal 8 × 8 × 11, or 704.
