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Jack is storing a rectangular box inside a cylindrical conta
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25 Nov 2020, 09:38
25 Nov 2020, 09:38
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Jack is storing a rectangular box inside a cylindrical container. The container has a volume of \(980\pi\) cubic inches and a height of 20 inches. Which of the following dimensions could the box have in order to fit inside the cylinder?
Indicate all such values.
A. 3 inches by 6 inches by 12 inches
B. 6 inches by 9 inches by 15 inches
C. 10 inches by 10 inches by 10 inches
D. 8 inches by 9 inches by 16 inches
E. 11 inches by 15 inches by 18 inches
F. 9 inches by 9 inches by 20 inches
Indicate all such values.
A. 3 inches by 6 inches by 12 inches
B. 6 inches by 9 inches by 15 inches
C. 10 inches by 10 inches by 10 inches
D. 8 inches by 9 inches by 16 inches
E. 11 inches by 15 inches by 18 inches
F. 9 inches by 9 inches by 20 inches
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Official Answer
A,B,D,F
Re: Jack is storing a rectangular box inside a cylindrical conta
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27 Nov 2020, 00:03
27 Nov 2020, 00:03
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Carcass wrote:
Jack is storing a rectangular box inside a cylindrical container. The container has a volume of \(980\pi\) cubic inches and a height of 20 inches. Which of the following dimensions could the box have in order to fit inside the cylinder?
Indicate all such values.
A. 3 inches by 6 inches by 12 inches
B. 6 inches by 9 inches by 15 inches
C. 10 inches by 10 inches by 10 inches
D. 8 inches by 9 inches by 16 inches
E. 11 inches by 15 inches by 18 inches
F. 9 inches by 9 inches by 20 inches
Indicate all such values.
A. 3 inches by 6 inches by 12 inches
B. 6 inches by 9 inches by 15 inches
C. 10 inches by 10 inches by 10 inches
D. 8 inches by 9 inches by 16 inches
E. 11 inches by 15 inches by 18 inches
F. 9 inches by 9 inches by 20 inches
After some pondering, this is what I got!
Let's say that the diagonal of the rectangular box is equal to the diagonal of the cylinder, which is \(14\)
taking least of the two values from each option and trying to see if it fits
Option A -> \(3^2 + 6^2 <= 14^2\)
Option B -> \(6^2 + 9^2 <=14^2 \)
Option C -> \(10^2 + 10^2 > 14^2\) --> It is greater. Cannot be fit into the cylinder
Option D -> \(8^2 + 9^2 <= 14^2\)
Option E -> \(11^2 + 15^2 > 14^2\) --> It is greater.Cannot be fit into the cylinder
Option F -> \(9^2 + 9^2 <= 14^2\)
General Discussion
Re: Jack is storing a rectangular box inside a cylindrical conta
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26 Nov 2020, 05:09
26 Nov 2020, 05:09
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Jack is storing a rectangular box inside a cylindrical container. The container has a volume of 980π cubic inches and a height of 20 inches. Which of the following dimensions could the box have in order to fit inside the cylinder?
using the volume's formula for cylinder r=7
assume a rectangular is inscribed in a circle with a radius of 7. each side of the rectangular is 7radi2
now the area of rectangular with sides of 7radi2 is 98. and the volume of box is 98*20=1960
check the answer choices that their products is 1960 or less and the product of two of them is less than 98
using the volume's formula for cylinder r=7
assume a rectangular is inscribed in a circle with a radius of 7. each side of the rectangular is 7radi2
now the area of rectangular with sides of 7radi2 is 98. and the volume of box is 98*20=1960
check the answer choices that their products is 1960 or less and the product of two of them is less than 98
