# Algebra

This diagram shows a solid metal cylinder.

The cylinder hasbase radius 2x and height 9x.
The cylinder is melted down and made into a sphere of radius r
Find an expression for in terms of x

1. 👍 0
2. 👎 0
3. 👁 455
1. Volume of cylinder = ( 2 x ) ² ∙ π ∙ 9 x = 4 x² ∙ π ∙ 9 x = 36 x³ ∙ π

Volume of a sphere with radius r = ( 4 / 3 ) ∙ π ∙ r³

Volume of cylinder = Volume of a sphere

36 x³ ∙ π = ( 4 / 3 ) ∙ π ∙ r³

Divide both sides by π

36 x³ = ( 4 / 3 ) ∙ r³

Multiply both sides by 3

36 x³ ∙ 3 = 4 ∙ r³

108 x³ = 4 ∙ r³

Divide both sides by 4

27 x³ = r³

r³ = 27 x³

r = ∛ (27 x³ )

r = 3 x

1. 👍 3
2. 👎 0

## Similar Questions

1. ### calculus

A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the cylinder increases and the radius r decreases. Assume that no clay is lost in the process. Suppose the height of the cylinder is

2. ### physics

A string is wrapped around a uniform solid cylinder of radius r. The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m. Note that the positive y

3. ### calc

When the height of a cylinder is 12 cm and the radius is 4 cm, the circumference of the cylinder is increasing at a rate of pie/4 cm/m in, and the height of the cylinder is increasing four times faster than the radius. How fast is

4. ### Physics

Four objects - a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell - each has a mass of 4.59 kg and a radius of 0.252 m. (a) Find the moment of inertia for each object as it rotates about the axes shown in the

1. ### Calculus

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 2 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your

2. ### Physics

A small metal cylinder rests on a circular turntable that is rotating at a constant speed. The small metal cylinder has a mass of 0.20kg, the coefficient of static friction between the cylinder and the turntable is 0.080, and the

3. ### Algebra

Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled 2/3 for the flowers to last the longest. Her cylinder vase has a radius of 3 in and a height of 8 in. Using the equation

4. ### Calculus

A cylinder is inscribed in a right circular cone of height 5.5 and radius (at the base) equal to 2 . A) What are the dimensions of such a cylinder which has maximum volume? B) What is the radius? C) What is the height?

1. ### chemistry

Titanium is used in airplane bodies because it is strong and light. It has a density of 4.55 g/cm^3. If a cylinder of titanium is 7.75 cm long and has a mass of 153.2 g, calculate the diameter of the cylinder. (V=pi*r^2*h, where V

2. ### physical

A solid cylinder has a radius of 0.051 m and a height of 0.0030. The cylinder is composed of two different materials with mass densites of 1950 kg/m3. If each of the two materials occupies an equal volume, what is the mass of the

3. ### Algebra

The volume of a right circular cylinder (think of a pop can) is jointly proportional to the square of the radius of the circular base and to the height. For example, when the height is 10.62 cm and the radius is 3 cm, then the

4. ### Math

Cylinder A has radius r and height h. Cylinder B has radius 2r and height 2h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A? I have no idea how to start doing this problem. Are there