Question

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.

Answer 1

Two answers:

Choice B) area of cylinder base is (1/4)(3.14)x^2

Choice E) height is 4x

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Step-by-step 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

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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.

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Side notes:

• Choice A is false because x/2 is the actual radius.
• Choice C is similar to B, but the 1/2 should be 1/4.
• Choice D is false as above we found h = 4x. It's likely this is a trick answer if you forget to square x/2 properly.

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