Volume Divided by Area

Volume is how much three-dimensional space a substance (solid, liquid, gas, or plasma) or shape occupies or contains, often quantified numerically using the SI derived unit, the cubic meter.

Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The surface area of a 3-dimensional solid is the total area of the exposed surface. (Source: From Wikipedia).

Use of Volume Divided by Area:

The term volume divided by area is used to find the a dimension of a solid.

For example,

In a sphere, volume divided by area gives the radius of the sphere.

Volume of sphere = `4/3 pi r^3`

Surface area of sphere = `4 pi r^2`

Volume divided by area = `(4/3 pi r^3)/(4 pi r^2)`

= `r/3`

In a cube, volume divided by area gives the side of the cube,

Volume of cube = a^3

Surface area of cube = 6a^2

Volume divide by area = `(a^3)/(6a^2)`

= `a/6`

In a cylinder, volume divided by area gives the radius of the cylinder

Volume of cylinder = `pi r^2 h`

Surface area of cylinder = `2 pi r h`

Volume divided by area = `(pi r^2 h)/(2 pi r h)`

= `r/2`

Example Problems for Volume Divided by Area:

Here, we are going to see some example problems to find the dimensions of solid shapes using volume divided by area.

Example 1

Find the side of a cube whose volume is 125 cubic meter and the surface area is 150 square meter.

Solution

For a cube, Volume divide by area = `a/6` = `125/150`

`a/6` = `5/6`

a = 6

So, the side of the given cube is 5 meters.

Example 2

Find the radius of a sphere whose volume is 2393.88 cubic centimeter, and the surface area is 865.26 square centimeter.

Solution

We know that, the volume divided by area in a sphere gives `r/3`

Here, volume of the sphere = 2393.88 cubic centimeter

Surface area of the sphere = 865.26 square centimeter

Volume divided by area; `r/3` = `(2393.88)/(865.26)`

r = `(2393.88)/(865.26)` * 3

r = 8.3

So, the radius of the given sphere is 8.3 centimeter.

Example 3

The volume and lateral surface area of a cylinder are 565.2 cubic feet and 188.4 square feet respectively. Find the radius of the cylinder.

Solution

We know that, the volume divided by area in a sphere gives `r/2`

Volume of the cylinder = 565.2 cubic feet

Lateral area of cylinder = 188.4 square feet

Volume divided by area; `r/2` = `(565.2)/(188.4)`

r = `(565.2)/(188.4)` * 2

r = 6

So, the radius of the cylinder is 6 feet.