1. Changing The Subject of a Formula
Practice Test on Topic 17 Changing the Subject of a Formula
Test on Topic 17
Changing The Subject of a Formula 1.
Change the subject of the following formula to the desired variable.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h) P D R A F m =
2L + 2W
a – b
a – 2b
2  rh
4x + c
to W.
to a.
to b.
to r
to c.
to x
to y 2.
(a) B =
2g2
change the subject of the formula to g 2.
(b) V =
c  2d 2
change the subject of the formula to d. 3.
The Volume of a sphere of radius r and height h is given by the formula 4 3
 r 2 h V =
(a)
If the radius is 3 inches and the height is 10 inches what is he volume of the sphere?
(b) If the volume of the sphere is 32 in3 and its height is 100 in what is the radius of the
cone? 4.
The formula for converting a temperature in Fahrenheit F into Centigrade C is C =
(a) If the temperature is 23oF what will it be in Centigrade?
(b) If the temperature is 250C what will it be in Fahrenheit?
Page | 1

2. Changing The Subject of a Formula Solutions
Practice Test on Topic 17 Changing the Subject of a Formula
Changing The Subject of a Formula Solutions 1.
Change the subject of the following formula to the desired variable.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h) P D R A F m =
2L + 2W
a – b
a – 2b
2  rh
4x + c
to W.
to a.
to b.
to r
to c.
to x
to y
Solution (a): P =
2L + 2W
P – 2L = =
W = 2W W
Subtract 2L to both sides
Divide both sides by 2
Switch the order
Solution (b): D =
a – b
D+b a = a
D+b
Add b to both sides
Switch the order
Solution (c): R =
a – 2b
R – a =
– b
Subtract a to both sides
– R+a = b
Multiply both sides by – 1 b =
a – R
Switch the order
2  rh
Solution (d): A = C
2h A = A C
2h
Divide both sides by 2πh
Switch the order
Solution (e): F =
4x + c
F – 4x = c
Subtract 4x to both sides c =
F – 4x
Switch the order
Page | 2

3. y B V2 Solution (f): F = 4x + c F – c F  c 4 x m = 4x x F  c 4
Practice Test on Topic 17 Changing the Subject of a Formula
Solution (f): F =
4x + c
F – c
F  c 4 x m = 4x x
F  c 4
Subtract c to both sides
Divide both sides by 4
Switch the order
Solution (g):
mx = y
Multiply both sides by x y m = mx
Switch the order
Solution (h):
mx = y
Multiply both sides by x y m x =
Divide both sides by m 2.
(a) B =
2g2
change the subject of the formula to g B 2 g = g2 g B 2 2.
(b) V =
c  2d 2
change the subject of the formula to d. V2
V2 – c
V 2  c 2 d =
c + 2d2
2d2 d2 d
V 2  c 2
Page | 3

4. Practice Test on Topic 17 Changing the Subject of a Formula3.
The Volume of a sphere of radius r and height h is given by the formula 4 3
 r 2 h V =
(a)
If the radius is 3 inches and the height is 10 inches what is he volume of the sphere?
(c) If the volume of the sphere is 32 in3 and its height is 100 in what is the radius of the
cone? 4 3
 r 2 h 4 3
Solution (a): V = =
(3.14) (3) 2 (10) =
376.8 in3
The sphere would have a volume of in3
Solution (b):
To solve his problem we change the subject of the formula to r and then we can
use this new formula to solve the given problem. 4 3
 r 2 h V =
4 r 2 h
3V =
Multiply both sides by 3 3V
4h = r2 r
Divide both sides by
Take the square root of both sides
Switch the order 3V
4h r
We can now solve the problem 3V
4h
3(32)
4(3.14)(100) 96
1256
r = = = =
inches
So the radius of the sphere will be inches
Page | 4

5. + 32 C = (c) If the temperature is 23oF what will it be in Centigrade?
Practice Test on Topic 17 Changing the Subject of a Formula 4.
The formula for converting a temperature in Fahrenheit F into Centigrade C is C =
(c) If the temperature is 23oF what will it be in Centigrade?
(d) If the temperature is 250C what will it be in Fahrenheit?
Solution (a): C = C =
– 5o
The temperature will be – 5o Centigrade.
Solution (b):
To solve his problem we change the subject of the formula to F and then we can
use this new formula to solve the given problem. C =
9C =
5(F – 32)
Multiply both sides by 9 C =
F – 32
Divide both sides by 5 = F
Add 32 to both sides F =
+ 32
Switch the order
We can now solve the problem F =
+ 32
The temperature will be 77o Fahrenheit.
Page | 5