Reverse Formulas

So here comes another blog entry. While I'm not entirely being dependent on my laptop, I'm prone to losing my hard copies of my shenanigans, so I had this file saved on my hard disk. I just thought of posting this in my blog not because I'm bragging: some other people might have made this, for sure. I just want to serve as some sort of help for those having a hard time in geometry. So, here they are.

Surface Area Reverse Formulas:

1. Cube: s = √ (SA/6)

Ex. 96 square cm = Surface Area
? = Side

Solution:
s= √ (SA/6)
s= √ (96/6)
s= √16
s= 4

2. Rectangular Prism: h = [(SA/2) – (LW)] / (L+W)

Ex. 800 square cm = Surface Area
20 cm = Length
12 cm = Width
? = Height

Solution:
h= [(SA/2) - (LW)] / (L+W)
h= [(800/2) - (20*12)] / (20+12)
h= (400-240) / (32)
h= 160 / 32
h= 5

Note: If L is missing, substitute H in its place. This also applies if W is missing.

3. Pyramid: L = [(SA-B)] / (P/2)

Ex. 208 square cm = Surface Area
64 square cm = Base
32 cm = Perimeter
? = Slant Height

Solution:
L= [(SA-B)] / (P/2)
L= [(208-64)] / (32/2)
L= 144 / 16
L= 9

Note: I'm still working on reverse formulas where B and P is missing, since substition won't work on this one. Sorry for the inconvenience.

4. Cylinder: h = (SA/2 πr) - r

Ex. 3297 square cm = Surface Area
15 cm = Radius
? = Height

Solution:
h= (SA/2 πr) - r
h= [(3297/(2*3.14)*15)] - 15
h= (3297/94.2) - 15
h= 35-15
h= 20

Note: I'm still working on formulas where radius is missing, since substitution won't work on this one. Sorry for the inconvenience.

5. Cone: L = [(SA - (πr^2)] / πr

Ex. 188.40 square cm = Surface Area
5 cm = Radius
? = Slant Height

Solution:
L= [(SA - (πr^2)] / πr
L= [(188.40 - (3.14*(5^2)] / 3.14*5
L= (188.40 - 78.5) / 15.70
L= 109.9 / 15.70
L= 7

Note: I'm still working on formulas where radius is missing.

Volume Reverse Formulas:

1. Rectangular Prism: L = V/ WH

Ex. 135 cubic cm = Volume
5 cm = Width
3 cm = Height
? = Length

Solution:
L= V/ WH
L= 135/ (5*3)
L= 135/15
L= 9

Note: Substitution is allowed here.

2.a Triangular Prism: H = (V/h) / B

Ex. 4125 cubic cm = Volume
0.15 cm = Base
55 cm = h
? = Height

Solution:
H= (V/H) / B
H= (4125/55) / 0.15
H= 75/0.15
H= 500

2.b h or B = [(V/H)*2)] / h or B

Ex. 78 cubic cm = Volume
6 cm = Height
10 cm = Base
? = h

Solution:
h= [(V/H)*2)] / B
h= [(78/6)*2)] / 10
h= 26/10
h= 2.6

3. Cylinder: h= V/(πr^2)

Ex. 37.68 cubic cm = Volume
2 cm = Radius
? = Height

Solution:
h= V/(πr^2)
h= 37.68/(3.14*4)
h= 37.68/12.56
h= 3

3.b r = √[(V/(πh)]

Ex. 5595.48 cubic cm = Volume
22 cm = Height
? = Radius

Solution:
r= √[(V/(πh)]
r= √[(5595.48/(3.14*22)]
r=√(5595.48/69.08)
r=√81
r= 9

4. Pyramid (Rectangular Base) L or W = (V*3/h) / L or W

Ex. 320 cubic cm = Volume
8 cm = Height
10 cm = Width
? = Length

Solution:
L= (V*3/h) / W
L= (320*3) / 8) / 10
L= (960/8) / 10
L= 120/10
L= 12

4.b Square Base: s= √[(V*3)/h)]

Ex. 64 cubic cm = Volume
3 cm = Height
? = s

Solution:
s= √[(V*3)/h)]
s= √[(64*3)/3)]
s= √(192/3)
s= √64
s= 8

4.c Triangular Base: B or h= [(V*3/H)*2)] / B or h

Ex. 6 cubic cm = Volume
3 cm = Height
3 cm = Base
? = Height of Triangle

Solution:

h= [(V*3/H)*2)] / B
h= [(6*3/3)*2)] / 3
h= [(18/3)*2)] / 3
h= (6*2) / 3
h= 12/3
h= 4

4.d Pyramid (Height Missing)

Rectangular Base: (V*3) / (LW)
Square Base: (V*3) / (s^2)
Triangular Base: (V*3) / (Bh/2)

5. Cone: h = (V*3) / (πr^2)

Ex. 301.44 cubic cm = Volume
6 cm = Radius
? = Height

Solution:
h= (V*3) / (πr^2)
h= (301.44*3) / (3.14*36)
h= 904.32 / 113.04
h= 8

5.b (Radius Missing) r= √(V*3)/(πh)

Ex. 100.48 cubic cm = Volume
6 cm = Height
? = Radius

Solution:

r= √(V*3)/(πh)
r= √(100.48*3) / (3.14*6)
r= √(301.44)/(18.84)
r= √16
r= 4

Note: I'm still studying about cubic roots, so I can't give out reverse formulas on Volume of Cube and Sphere as of now.

Another note: I formulated these stuff on my trusty notebook during my vacation, so think twice before claiming I'm a plagiarist, seriously.