# MODELING THE VOLUME OF A SPHERE

## About "Modeling the volume of a sphere"

Modeling the volume of a sphere :

A sphere is a three-dimensional figure where all the points on the sphere would be at the same distance from the center. The radius of a sphere is the distance between the center to any point on the sphere.

## Modeling the volume of a sphere

We already know that a cone can fill one-third of a cylinder of where the radius and height of the cone and cylinder would be same.

If we do a similar experiment with a sphere of the same radius that the cylinder has, we will find that the sphere can fill two-third of the cylinder.

Here, the cylinder’s height would be equal to two times the the radius of the sphere.

Step 1 :

Write the formula for volume V of a cylinder with base area B and height h.

V  =  B · h

Step 2 :

Find the base area B of the cylinder.

We know that the base of the cylinder is a circle (Look at the figure given below).

So, the area of the base of a cylinder is

B = r²

Step 3 :

Write the formula for volume V of a cylinder with base area B r² and height h.

V  = r²h

Step 4 :

A sphere of the same radius that the cylinder has, we will find that the sphere can fill two-third of the cylinder.

So, we have

Volume of sphere  =  2/3 · Volume of cylinder

Volume of sphere  =  2/3 · r²h

(Here, radius and height of the sphere and radius and height of the cylinder are equal)

Step 5 :

A sphere always has a height which is equal to twice the radius.

So, substitute 2r for h.

Volume of sphere  =  2/3 · r²(2r)

Simplify.

Volume of sphere  =  4/3 · r³

## Reflect

A cone has a radius of r and a height of 2r. A sphere has a radius of r. Compare the volume of the sphere and cone.

The cone’s volume is one-third of a cylinder with radius r and height 2r. The sphere’s volume is two-third of the volume of this cylinder. So, the sphere’s volume is twice the cone’s volume.

After having gone through the stuff given above, we hope that the students would have understood, how to model the volume of a sphere.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6