# MODELING THE VOLUME OF A CONE

## About "Modeling the volume of a cone"

Modeling the volume of a cone :

A cone is a three-dimensional figure that has one vertex and one circular base as shown in the figure given below.

In this section,, we are going to see, how the volume of a cone can be modeled.

## Modeling the volume of a cone

To explore the volume of a cone, Alexa does an experiment with a cone and a cylinder that have congruent bases and heights. She fills the cone with popcorn kernels and then pours the kernels into the cylinder as shown in the figure.

She repeats this until the cylinder is full.

Alexa finds that it takes 3 cones to fill the volume of the cylinder.

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 cone.

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

So, the area of the base of a cone is

B = r²

Step 3 :

Alexa found that, when the bases and height are the same,

3 x Volume of cone  =  Volume of cylinder

Step 4 :

From step 3, solve for volume of cone.

3 x Volume of cone  =  Volume of cylinder

Divide both sides by 3.

(3 x Volume of cone) ÷ 3  =  Volume of cylinder ÷ 3

Volume of cone  =  1/3 · Volume of cylinder

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

## Reflect

1. Use the conclusion from this experiment to write a formula for the volume of a cone in terms of the height and the radius. Explain.

Volume of the cone  =  1/3 · Volume of cylinder

Substitute the formula for volume of cylinder.

Volume of the cone  =  1/3 · r²h

2. How do you think the formula for the volume of a cone is similar to the formula for the volume of a pyramid ?

Both are one third the area of the base times the height.

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

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