How do i find the diameter and circumference when given the area?

Hello from MrBillDoesMath!

Diameter = 2r = 2 (sqrt(24/Pi))

Circumference =  4 sqrt(6Pi)

Discussion:

Given:

     Area  of circle =  Pi r^2

               24 = Pi r^2        =>  (as Pi r^2 is the formula for area of a circle)

               24/Pi = r^2       =>  ( now take the square root of both sides)

               r= sqrt(24/Pi)

Diameter = 2r = 2 (sqrt(24/Pi))

Circumference = 2 PI r = 2Pi (sqrt(24/Pi))

                                       = 2Pi (sqrt(24)/sqrt(Pi) )

                                       = 2Pi (2sqrt(6)/sqrt(Pi) )

                                       =  4 (pi/ sqrt(Pi) ) sqrt(6)

                                       = 4 sqrt(Pi) sqrt(6)

                                       = 4 sqrt(6Pi)

Thank you,

MrB

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this