Maria needs to fill an empty storage container with wooden cubes measuring 2 centimeters across each face. the container is in the shape of a cube 10 centimeters wide. how many wooden cubes does maria need to fill the container?

Maria needs 125 wooden cubes to fill the container

Step-by-step explanation:

Given : Dimension of wooden cube : 2 cm

          Container which is cube shaped is 10 cm wide.

To Find: How many wooden cubes does Maria need to fill the container?

Solution:

Volume of cube

Where x is the side length.

So, volume of wooden cube =  

                                               =  

Thus the volume of wooden cube is 8

Volume of cube shaped container =  

                                                        ==  

So, maria needs wooden cubes to fill the container :

=

=

=

Hence Maria needs 125 wooden cubes to fill the container

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

6 on both sides and twelve on the top and the bottom

step-by-step explanation: