The edge of each cube used to build this rectangular prism is 1/3 inch long. Which equation shows the volume of the prism, in cubic inches?
|A|(9/3⋅6/3⋅6/3) in.^3 = 12 in.^3
|B|(3/3⋅2/3⋅3/3) in.^3 = 2/3 in^.3
|C|(3 1/3⋅2 1/3⋅3 1/3) in.^3=25 25/27 in.^3
|D|(3⋅2⋅3) in.^3=18 in.^3

Option B

Step-by-step explanation:

step 1

Find the number of cubes in the prism

step 2

Find the volume of one cube

The volume of one cube is equal to

where

b is the length side of the cube

we have

substitute

step 3

To find out the volume of the prism , multiply the volume of one cube by the number of cubes

so

simplify

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this