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.
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.
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
If the original length of the side of a cube were 5.42 inches it would be difficult to cut 7 inches off it!!
Oh. Very sorry. I'm only a 6th grader. I sometimes make Calculation Errors/Properties.
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).
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)?