How does the shape of a cross-section of a 3D figure parallel to the base relate to the volume of the 3D figure?

The volume of  a 3D figure can be determined by the sum of  all the cross-sections of that 3D figure parallel to the base

Step-by-step explanation:

We need to understand what a cross-section of a 3D figure ?

A cross section is the shape we get when cutting straight through an object

and in geometry it is the shape made when a solid is cut through by a plane.

=> the cross section is parallel to the base of the figure.

So that the area of the cross-section is determined by its shape

Hence, The volume of  a 3D figure can be determined by the sum of  all the cross-sections of that 3D figure parallel to the base  

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3