The object below is made up of identical cubes. each cube has edges that are 5 feet long. • what is the perimeter of the base of the object? show all your work and explain your reasoning. be sure to label your answer with the correct units. • what is the volume of the object in cubic feet? show all your work and explain your reasoning.

P = 60 ft

V = 625 ft³

Step-by-step explanation:

Perimeter of the base:

The perimeter means the total length of the outside of a shape. The base is also called the "bottom". Although we can't see the bottom in the picture, it's also the same as the top.

Count how many outside edges there are on the top of the shape. There are 12 outer edges.

Since each edge is 5 feet long, multiply the number of edges by the length of each edge.

12 edges X 5 ft = 60 ft

The perimeter of the base is 60 feet.

Volume of the object:

The formula for the volume of a cube is V = s³. "s" means the length of one edge.

We know an edge is 5 feet. Use this in the formula to find the volume of one cube.

V = s³

V = (5ft)³

V = 125ft³

Now, count the number of cubes. There are 5 cubes. All of the cubes are the same, so we multiply the volume of 1 cube by the number of cubes.

= 5 cubes X 125ft³

= 625ft³

The volume of the shape is 625 cube feet.

Your perimeter is 60 feet and you volume is 625 feet,

Step-by-step explanation:

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

i think the correct option is the second option.