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A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar

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by VJesus12 » Fri Nov 27, 2020 12:54 am

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A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?

(A) 20
(B) 40
(C) 60
(D) 80
(E) 100

Answer: D

Source: Official Guide
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Re: A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a simi

by swerve » Fri Nov 27, 2020 4:06 pm
VJesus12 wrote: ↑
Fri Nov 27, 2020 12:54 am
 A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?

(A) 20
(B) 40
(C) 60
(D) 80
(E) 100

Answer: D

Source: Official Guide
Volume \(= l \cdot b \cdot h = 10 \, ft^3\)
Now we have twice as long, twice as wide, and twice as high as the first sandbox,
\(L=2\cdot l\)
\(B=2\cdot b\)
\(H=2\cdot h\)
Final volume \(=L\cdot B\cdot H =2\cdot l\cdot 2\cdot b\cdot 2\cdot h = 8\cdot (l\cdot b\cdot h) =8\cdot 10=80 \,ft^3\)

Therefore, D
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