Answer please

The answer is below

Step-by-step explanation:

1) The volume of the cylinder = πr²h; where h is the height and r is the radius.

The volume of the cone = πr²h/3 = volume of cylinder / 3 = 78 cm³ / 3 = 26 cm³

2) The volume of the square pyramid = a²h/3; where h is the height and a is the side length of the square base.

The volume of the square prism = a²h = volume of the square pyramid * 3 = 36 cm³ * 3 = 108 cm³

3) The volume of the cylinder = πr²h; where h is the height and r is the radius.

The volume of sphere = 4/3(πr³)

but the height of cylinder = diameter of sphere = 2r. Hence r = h/2

Volume of sphere= 4/3(πr² * h/2) = 2/3(πr²h) = 2/3 * volume of cylinder = 2/3 * 198 m³ = 132 m³

4) The volume of sphere = 4/3(πr³)

but the height of cylinder = diameter of sphere = 2r. Hence r = h/2

Volume of sphere= 4/3(πr² * h/2) = 2/3(πr²h)

Volume of cylinder = πr²h = volume of sphere * 3/2 = 67.5 m³ * 3/2 = 101.25 m³

The volume of the square pyramid = a²h/3; where h is the height and a is the side length of the square base.

The volume of the square prism = a²h = volume of the square pyramid * 3 = 45.5 m³ * 3 = 136.5 m³

equal to

step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be