Fsc Part 2 Mathematics (Complete Solutions)
Q3
Express the following
(a) The perimeter P of square as a function of its area A.
(b) The area A of a circle as a function of its circumference C.
(c) The Volume V of a cube as a function of the area A of its base.
(b) The area A of a circle as a function of its circumference C.
(c) The Volume V of a cube as a function of the area A of its base.
Solutions
(a) The perimeter P of square as a function of its area A.
if 'x' is the unit of the side of the square.
Then its perimeter P = x + x + x + x
P = 4x  (i)
Area of the Square = A = x.x
A = x^{2}

= 

x  = 

 (ii) 
Put the valus of x in equation (ii)
P = 4
√  A 
(b) The area A of a circle as a function of its circumference C.
radius of the circle = x
Area of the Circle = A
A = π x^{2}  (i)
Circumference = C = 2π x
x = 

 (ii) 
Putting the value of 'x' in equation (i), A = π x^{2}
A = π  ( 

) ^{2} 
A = π 

A = 

C^{2} 
(c) The Volume V of a cube as a function of the area A of its base.
Let x unit be each side of cube.
The volume of Cube = V = x . x . x
V = x^{3}  (i)
Area of Base = A = x^{2}
x = 

 (ii) 
Put the value of x in equation (i)
V =  ( 

)^{3} 
V =  (A) ^{3/2} 