16 cm 12 cm
radius of cylinder = 5 cm
radius of cone = 4 cm
A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder
as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of pl'.)

Step-by-step explanation:

volume  of cylinder = πr²h = π(5²)(16) ≅ 1256 cm³

volume of cone = ⅓πr²h = ⅓π(3²)12 ≅ 113.04 cm³

volume of air space = 1256 - 113.04 = 1143.96 cm³

(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