A cylinder with a base diameter of x units has a volume of πx3 cubic units.

Which statements about the cylinder are true? Check all that apply.

(1) The radius of the cylinder is x units.

(2) The radius of the cylinder is 2x units.

(3) The area of the cylinder's base is πx2 square units.

(4) The area of the cylinder's base is πx2 square units.

(5) The height of the cylinder is 2x units.

(6) The height of the cylinder is 4x units.

Question

Mathematics

Yair Collins

9 January, 04:35

A cylinder with a base diameter of x units has a volume of πx3 cubic units.

Which statements about the cylinder are true? Check all that apply.

(1) The radius of the cylinder is x units.

(2) The radius of the cylinder is 2x units.

(3) The area of the cylinder's base is πx2 square units.

(4) The area of the cylinder's base is πx2 square units.

(5) The height of the cylinder is 2x units.

(6) The height of the cylinder is 4x units.

+3

Answers (2)

Know the Answer?

Gavin Esparza · Answer 1

The volume of the cylinder:

V = r² π h

We know that a base diameter: d = x

r = d / 2 = x / 2

π x³ = (x/2) ² π h

π x³ = x²/4 π h / : π

x³ = x²/4 h

h = x³ : x²/4 = x³ · 4/x²

h = 4 x

As for the base: B = r² π = (x/2) ² π = π x² / 4

Answer:

Correct statement is:

(6) The height of the cylinder is 4 x units.

Naima Wallace · Answer 2

The answer:

The answer:

The volume of a cylinder formula is given by V = Pi r² h

If the base diameter has x units, so the radius = r = diameter / 2 = x/2

It was given that the volume is v = πx3, so we can deduce that v = πx3=Pi r² h, and from where

X3 / x²/4 = h then h = 4x.

the true answer is

(6) The height of the cylinder is 4x units.