how do i solve for x with the measurements http://s292.photobucket.com/albums/mm9/xodarlenexo/?action=view&current=untitled-1.jpg

Expert Answers
hala718 eNotes educator| Certified Educator

For the rectangular prism:

You have the measures:

10 , 12 , and (x)

We know that the volume (v)= Length*width*height)

==> 10*12*x= 283

==> 120x=283

==> x=283/120= 2.36 ft

For the cylinder:

The volume (v)= pi*h*r^2 , where h is the height and r is the radius.

==> 300= pi*10*x^2

pi=3.14

==> x^2= 300/10*pi = 9.5

==> x= 3.09 m

 

 

neela | Student

Firrst picture:

A rectangular box, whose base is 10 ft by 12ft and unknown height say h . Another  box of base  is (10-x)ft  by  (12 -x)ft and the height  h , is  kept inside the box. The inner box occupies a space of 97% of the outer box whose volume is283 cubic feet. To find the height and x.

Solution:

The bigger outer box: Volume = 10*12*h = 283. Or h = 283/10*12 =2.35833...

Inner box: Volume = (10-x)(12-x)h = 97%{283} Or

120-22x+x^2 = 0.97(283)/h = 116.4. Or

x^2-22x+120-116.4 = 0.

x^2-22x+3.6 = 0.

x1 = [22+sqrt(22^2 - 4.3.6)]/2   or

x2 =   [22-sqrt(22^2 - 4*3.6)]/2 =  0.164871943 is the practical solution.

2 picture:

To find the radius x of cylinder whose height is 10m and volume is 300 m^3.

The  volume V,  radius  r, and the length l , of a cylinder are connected by the formula:

V  = Pi*r^2*h. Making r the subject, we get:

r = sqrt[ V/(pi*h)]. Substituting the given values V = 300m^3, and r = 10m, we get:

h = sqrt[300/(Pi*10)] = sqrt[300/(10pi)] = 3.090193616 m

Hope this helps.

V = pi*