Look at the three-dimensional figure.

The volume of the prism is the amount of space _ the figure.

a). around
b). inside
c). outside

120 cubes fit inside the prism, so the figure has a volume of _ square units.

a). 60
b). 80
c). 120

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Answers:

Option (B) and Option (C)

Explanation:

The volume of a 3D shape is the amount required to 'fill' the figure.

"around" would be perimeter, and "outside" would be surface area.

Going from question one, 120 cubes fit the prism. This means that the prism is 120 units³.

Extra note:

Volume is measured in cubic units, not square units, like the question stated.

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

answer: d. $20

step-by-step explanation:

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