8solid iron sphare with radius 'a cm' each are melted to form a sphare with radius 'b cm'. find the ratio of a: b

8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm' then the ratio of a:b is 1 : 2

Solution:

Given that 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'

Need to find the ratio of a:b

As 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'.  

For sake of simplicity, let volume of 1 sphere of radius a cm is represented by and volume of 1 sphere of radius b cm is represented by

So volume of 8 solid iron sphere with radius 'a cm' = volume of  1 solid iron sphere with radius 'b cm'

 ---- eqn 1

Formula for volume of sphere is as follows:

Where r is radius of the sphere

Substituting r = a cm in the formula of volume of sphere we get

Substituting r = b cm in the formula of volume of sphere we get

a : b = 1 : 2

Hence the ratio of a:b is 1 : 2

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

i believe the correct answer is b.