A cylinder with a base diameter of x units has a volume of
3.14x^3 cubic units
Which statements about the cylinder are true? Select two
options.
The radius of the cylinder is 2x units.
The area of the cylinder's base is 1/4•(3.14)•x^2 square units.
The area of the cylinder's base is 1/2•(3.14)•x^2 square units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.

Explanation:

The area of a circle is pi*r^2 with r as the radius. The diameter given is x, so half of this is x/2 which is the radius. So r = x/2

The area of the base is

pi*r^2 = pi*(x/2)^2 = pi*(x^2)/4 = (1/4)pi*x^2 = (1/4)(3.14)x^2

Use this with the volume to find the height

volume of cylinder = (area of base)*(height)

V = (pi*r^2)*h

V = (1/4)(3.14)x^2*h

3.14x^3 = (1/4)(3.14)x^2*h

x^3 = (1/4)x^2*h divide both sides by 3.14

x = 1/4*h divide both sides by x^2

4x = h multiply both sides by 4

h = 4x

The height is 4 times the diameter.

Side notes:

All of these facts allow us to cross these answer choices off the list.

step-by-step explanation:

answers available in this download

(pearson%2c%25202012)%2520bbs.pdf& usg=aovvaw1obmtxnfghfgxhx0urh_je

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!