The volume of a pyramid with a square base, where the perimeter of the base is 7.3\text{ ft}7.3 ft and the height of the pyramid is 11.1\text{ ft}11.1 ft

12.21ft³

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, square based pyramid.

Volume of square based pyramid is expressed as

V= a²(h/3)

Given data

Perimeter p = 7.3ft

Height h= 11.1ft

Since the shape has a square base let us solve for the length of each side

Perimeter of square p = a+a+a+a

p= 4a

7.3= 4a

a= 7.3/4

a= 1.83ft

Substituting our given data we have

Volume = 1.83²(11.1/3)

V= 3.3*3.7

V= 12.21ft³

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

could

step-by-step explanation:

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