A carpenter constructed a rectangular sandbox with a

Question

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

Practice Questions
Question: 18
Page: 154
Difficulty: 550

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

Bunuel · Accepted Answer

SOLUTION

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

Practice Questions
Question: 18
Page: 154
Difficulty: 550

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

Since given that  volume=L*W*H=10 , then  new \ volume=(2L)*(2W)*(2H)=(2*2*2)*(L*W*H)=8*10=80 .

Answer: D.

SOURH7WK · Answer

Let x,y & z be L,W & H
so xyz = 10 cu ft
As per question if we double the lengths on all dimensions
we get (2x)(2y)(2z)=8 xyz= 8*10= 80
Answer: D

abhi398 · Answer

volume =l*b*h =10 cubic feet
Now we have twice as long, twice as wide, and twice as high as the first sandbox, 
L=2*l
B=2*b
H=2*h
final volume =L*B*H =2*l*2*b*2*h=8*(l*b*h) =8*10=80 cubic feet

answer is D

ashish8 · Answer

V=LWH

Original Volume = 10

In order to keep things simple. I made Height = 5, Length = 2, and Width = 1

The second statement says double everything.

Height = 10, Length = 4, and Width = 2

V = 80

OmniPrep · Answer

A quick note on doubling. When you double a length you have 2*L1. When you double all lengths of a rectangle you have (2*L1)(2*L2) = A. An increase of 2^2 or 4. When you double all lengths of a rectangular prism you have (2*L1)(2*L2)(2*L3) = V. An increase of 2^3 or 8.

This leads to the basic relationship:

Line: 2*original size
Rectangle: 4*original size
Rectangular Prism: 8*original size

You can do the math out or memorize this relationship to speed things up.

PareshGmat · Answer

Answer = (D) 80

Original volume = 10 cubic feet

All 3 dimensions made "twice"

New volume = 10 * 2 * 2 * 2 = 80

ScottTargetTestPrep · Answer

We are given a rectangular sandbox with a given capacity, which is the volume of the sandbox.

Therefore, we know that the volume of the sandbox is: (L)(W)(H) = 10 cubic feet

We then are told that the carpenter doubles the length, the width, and the height. We can represent this doubling as (2L)(2W)(2H). Thus

(2L)(2W)(2H) = (2)(2)(2)(L)(W)(H) = (2)(2)(2)(10) = 80 cubic feet

Answer D.

sasyaharry · Answer

Using some simple values, let all sides be equal to 2. The first surface area will be 2*2*2 = 8
Now double all these sides. The new surface area will be 4*4*4=64
64 is 8*8. Hence the answer should be 10*8=80 or  D

longhaul123 · Answer

I have a small doubt in this question. The volume of a rectangular solid is l*w*h=10*10*10 because the question says its cubic feet. Where am i going wrong in my concept??

Bunuel · Answer

We are told that the volume is 10 cubic feet (the volume of 3-D objects is measured in cubic units), not that the lengths of the sides are 10 feet, so it should be l*w*h = 10. Please re-read the solutions above.

longhaul123 · Answer

Thank you Bunuel .

Rocket7 · Answer

This may is more of a conceptual question I guess. In 2l *2b*2h can we not take the 2 common such as 2(L*B*H).

L*B*H=10.....-> given.

2L*2B*2H= ?
2(L*B*H)
2(10)=20

dixxa · Answer

I have a similar question. Why are we not taking the common factor 2(L*B*H)?

PKN · Answer

Hi  dixxa ,
Common factors are to be factored out when the terms are either added or substracted in an equation/expression. In case of multiplication or division, it is simply multiplication or division of terms respectively.

Here, in 2L*2B*2H, we have three terms multplied 2L, 2B, and 2H.

From 2L, 2 can be factored out. (you know 2L=2 multiplied by L)

Similarly, From 2B, 2 can be factored out.
Similarly, From 2H, 2 can be factored out.

Now, 2L*2B*2H=2*2*2*L*B*H=8(L*B*H)

Had it been 2L+2B+2H, then we can factor out 2 as '2' is a common factor of 2L, 2B, and 2H, making 2L+2B+2H=2(L+B+H)

Hope it clarifies your query.

dixxa · Answer

Thank you so much for your explanation. It makes sense.

LMP · Answer

If each of the sides was increased by a factor of 2,

then the linear ratio is 1:2. In order to get the volume ratio, I need to

cube the linear ratio; so the volume ratio is going to be (1 cubed), to (2 cubed) -- which is 8.

So if this is 10 cubic feet, this is going to be 80 cubic feet, and the correct answer choice is D.

ArnauG · Answer

The capacity of a rectangular sandbox is calculated by multiplying its length, width, and height.

Let's denote the length, width, and height of the first sandbox as L, W, and H, respectively.

We are given that the capacity of the first sandbox is 10 cubic feet, so we have the equation L * W * H = 10.

Now, the carpenter wants to make a second sandbox that is twice as long, twice as wide, and twice as high as the first sandbox.

The dimensions of the second sandbox would be 2L, 2W, and 2H, respectively.

The capacity of the second sandbox can be calculated as (2L) * (2W) * (2H) = 8 * L * W * H.

Capacity of the second sandbox = 8 * L * W * H = 8 * 10 = 80 cubic feet.

Therefore, the capacity of the second sandbox is 80 cubic feet, corresponding to option (D).

bumpbot · Answer

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A carpenter constructed a rectangular sandbox with a

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