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A 7in thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 67in^3 . Use a graphing calculator to find the side length of the original cube. Round your answer to two decimal places.

 Mar 24, 2016

Best Answer 

 #2
avatar+33665 
+5

If the original side length is L inches, then we have

 

L^2(L-7) = 67

 

This gives a value for L of 8.04 inches (to 2dp).

 Mar 25, 2016
 #1
avatar+426 
0

Let the volume of the cube be v in3 (I am studying in Singapore, so I use cm more frequently. ).

Note: a / b = a divided by b (fraction form)

 

v1 / 3 - 7 in = 67 in3/ (v2 / 3)

 

v = (v1 / 3)3

Rewrite equation in this form:

v = { [67 in3 / v(2 / 3) + 7 in] }3

 

Simplifying yields:

 

v5 / 3 - 7v2 / 3 - 67 = 0

 

Shift term 0 to the left:

 

v5 / 3 - 7v2 / 3 = 67

 

Rewrite equation in this form as a - b = c, and a - c = b:

 

v5 / 3 - 67 = 7v2 / 3

 

Divide it by 7:

 

(v5 / 3 - 67) / 7 = v2 / 3

Finding v:

[(v5 / 3 - 67) / 7]3 / 2 = v

Split the fraction into two parts, as (a-b) / c = (a / c) - (b / c):

[(v5 / 3 / 7) - (67 / 7)]3 / 2 = v

 

 

Simplified to decimal form:

(v - 12.46363958)/7 = v3 / 5

 

v/7 - 1.78051994 = v3 / 5

 

(0.14285714v - 1.78051994) = v3 / 5

 

0.14285714 v5 / 3 - 2.615640598 = v

 

v + 2.615640598 = (0.14285714 v5 / 3)

 

Hmm... Cant seem to find v1 / 3. Will have Part 2 if i have.

 Mar 25, 2016
 #4
avatar+426 
0

Part 2:

 

By using photo math, we found out that

 

(v - 673 / 5) / 7 = v3 / 5

 

and

 

v ≈ 158.993142

v1 / 3 = 5.417423624 ≈ 5.42 in

 

Answer: 5.42 in

MWizard2k04  Mar 26, 2016
 #5
avatar+33665 
0

If the original length of the side of a cube were 5.42 inches it would be difficult to cut 7 inches off it!!

Alan  Mar 26, 2016
 #10
avatar+426 
0

Oh. Very sorry. I'm only a 6th grader. I sometimes make Calculation Errors/Properties.

MWizard2k04  Mar 27, 2016
 #11
avatar+33665 
0

No problem; we all make mistakes.  This example shows that it's important to check your results wherever possible.

Alan  Mar 27, 2016
 #2
avatar+33665 
+5
Best Answer

If the original side length is L inches, then we have

 

L^2(L-7) = 67

 

This gives a value for L of 8.04 inches (to 2dp).

Alan Mar 25, 2016
 #6
avatar+33665 
+5

The Microsoft Mathematics graphing calculator shows the following:

 

graph

.

Alan  Mar 26, 2016
 #7
avatar+118724 
0

Hi, Alan,  I found this site,

 

https://www.microsoft.com/en-au/download/details.aspx?id=15702

 

Is this a free calculator ?  Sometime I download things but then I cannot install unless I pay ://

Have you used this calc much.  Have you found it better than the others we already use (for some applications)?

 Mar 26, 2016
 #8
avatar+33665 
0

Yes this is the right one Melody. It is free.

Alan  Mar 26, 2016
 #9
avatar+33665 
0

It is a graphing calculator, which is fairly easy to use. Like all these things it has good and bad features! 

Alan  Mar 26, 2016

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