 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.

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 = x2
 √ A
=
 √ x2
x =
 √ A
------------------------------ (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 x2 ------------------------------ (i)
Circumference = C = 2π x
x =
 C 2π
------------------------------ (ii)
Putting the value of 'x' in equation (i), A = π x2
A = π (
 C 2π
) 2
A = π
 C2 4π2
A =
 1 4π
C2

(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 = x3 ------------------------------ (i)
Area of Base = A = x2
x =
 √ A
------------------------------ (ii)
Put the value of x in equation (i)
V = (
 √ A
)3
 V = (A) 3/2