Calculating Volume of Cylinders, Cones, Pyramids, and Spheres

[Applause] math 6 quarter

4 week 2 milk base let's learn about volume of solid figures this is

from Learners packet lip hello kids it's me teacher FR don't forget to

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Facebook page teacher FR TV for today's lesson in math 6 we will discuss about volume of solid

figures for most essential learning competencies finds the volume of cylinders pyramids cones and

Spears and solves routine and non-routine problems involving volumes of

solids hello in this lesson we will study and learn about the volume of solid figures and solves routine and

non-routine problems involving volumes of solids we will derive formulas to

calculate for the volume in cubic units let us try to build a connection and and derive a formula between the

volume of these matching solids same radius and same height suppose that we will try to fill these solid figures

with water or sand here is a trivia do you know that it takes three cones to fill the

cylinder with sand or water another trivia the space of a spear takes 2/3 of the volume of the

cylinder the remaining space of the cylinder is 1/3 another trivia it takes exactly

three full pyramids to fill the prism note volume of a cylinder is three times the volume of the cone or the

volume of a cone is 1/3 that of the cylinder what is the formula to be used to find the volume of a cylinder the

formula is volume equals base time height where base is equals to the area of the base where the formula of the

base is pi = radius square or use 3.14 for pi so the formula for the volume is piun * radius square *

height what mathematical formula can you derive from the volume of a cone how do we write the formula for the volume of a

cone so the formula for the volume of of a cone is volume equal 1/3 base * height where base is the area of the base or

base equals Pi radius squar use 3.14 for pi H is the height of the cone so the formula is volume equal base * height /

3 or 5 * radius square * height / 3 or 1/3 * > * radius square and now let us study example

number one this is the volume of a cone let's read the problem a cone hat has a diameter of 5 cm and a height of 10 cm

what is its volume what is being s the volume of the cone what are the given facts

diameter equal 5 cm and height equals 10 cm what is the operation to be use the operation to be used is the

formula for the volume of a cone which is volume equal 1/3 base * height or 1/3 = Pi radius squar what is the number

sentence the number sentence is volume equal 1/3 base * height or 1/3 3 piun radius squ =

n now write the solution with the correct label the radius of this cone is 2.5 cm

because the diameter is 5 cm divided by 2 and that is 2.5 cm formula volume = 1/3 base height or 1/3 Pi radius square

1/3 * 3.14 which is pi * multip by the radius 2.5 then the height is * 10 cm multiply the radius by itself 2.5 cm *

2.5 cm = 6.25 CM now multiply 6.25 * 10 = 62.5 then multiply 3.14 * 62.5 =

19625 divided by 3 equal 6542 cubic cm so the volume of the cone is

6542 cubic cm example number two volume of a cylinder Bobby is molding a cylindrical

candle with a diameter of 12 CM and a height of 18 cm how much wax does he need to mold the

candle what is the shape of the candle the shape of the candle is cylinder how are you going to solve the

problem find the volume of the cylindrical candle and what is the formula for the

volume of a cylinder the formula is volume = < * radius square * height Write Your solution and answer so

this is the formula for the volume of a cylinder Pi is equivalent to 3.14 the radius is 6 for the diameter is

12 CM ided by 2 and that is 6 and the height is 18 cm multiply the radius by itself 6 * 6 = 36 multiply 3.14 * 36

= 13.04 then multiply 113.04 * 18 =

23472 cubic cm Bobby needs 23472 cubic cm of wax to mold the

candle example number three volume of a pyramid the volume of a pyramid is given by the formula

volume of pyramid equals 1/3 * area of base time height in a chang or Bazaar Joshua bought a square pyramid glass

keychain for his bag the base of the keychain is 3 cm by 4.5 CM its height is 6 cm find the volume of the glass used

to make the glass pyramid what is being asked the volume of the glass pyramid k

chain what is the shape of the base the shape is rectangle what are the given facts 3 in

by 4.5 in and the height is 6 in what is the operation to be used the formula for the volume of

pyramid and here is the formula for the volume of a pyramid volume = 1/3 base * height or

volume = 1 thir length * WID * height solution and answer so volume equal 1/3 * base 3x 4.5

and * the height which is 6 so 3 * 4.5 = 13.5 then multiply 13.5 * 6 / 3 = 27 cubic

cm the volume of the glass per pyramid keychain is 27 cubic cm example number four volume of spear

Jackie wants to know how much water a spear can hold with a radius of 8 cm find the volume use 3.14 for pi so what

is being asked the volume of the water the spear can hold what are the given facts radi juuse equals 8 C CM what is

the operation to be used the formula for the volume of a sphere and this is the formula volume

equal 4/3 * radius cubic write the number sentence and your final answer with its correct label so

this is the formula volume = 4/3 * 3.14 which is the pi * 8 which is the radius and multiply

8 by itself three times so 8 * 8 * 8 = 512 then multiply 3.14 * 512 = 1, 16768 then multiply 1,

16768 ultip by 4 and then divided by 3 the answer is 24357 cub cubic

cm so the volume of the water the spear can hold is 2,143 57 cubic

cm remember the volume of a solid figure is the amount of space inside it volume is measured in cubic units which are

cubic M cubic cm cubic decim Etc which means the total number of Cubes it takes to fill a solid

figure and now let us proceed to learning test one find the volume of each solid figure use 3.14 for pi Show

Your solution and answers in your notebook so find the volume of a cylinder with a radius of 3.5 M and the

height is 8 m the formula for the volume of a cylinder is volume = < radius square height volume =

3.14 < * 3.5 the radius and 8 m the height now multiply 3.5 by itself so 3.5 * 3.5 =

12.25 and then multiply 3.14 * 12.25 = 38400 65 then multiply by 8

38465 * 8 = 37.72 cubic M and this is the volume of a

cylinder now get the volume of spere the radius is 20 DM the formula for the volume of spere

is volume = 4/3 * radius to the 3 power or 4 3 * 3.14 which is the pi * 20 which is the radius multiply 20 by itself 3 *

20 * 20 * 20 = 8,000 3.14 * 8,000 = 25,124 * 25120 ided by 3 = 33,400

9333 cubic decim and this is the volume of a sphere Now find the volume of a pyramid

with a length of 3.5 in width is 1.5 in and the height is 4 in the formula is volume = 1/3 base * height or volume =

1/3 length * WID * height solution and answer 1/3 multiply the length and the width

which is 3.5 * 1.5 = 5.25 then multiply 5.25 * 4 4 is the height 5.25 * 4 / 3 =

7 cubic in so this is the volume of a pyramid Now find the volume of a cone with the height of cm and the radius is

7 m so volume equal 1/3 base * height or 1/3 piun radius squar 1/3 5K is 3.14 * the radius which is 7 ultip by itself *

20 which is the height so 7 * 7 = 49 then multiply 49 * 20 = 980 then multiply 3.14 * 980 =

3772 then divide by 3 equal 1 12573 cbic M this is the volume of a cone for learning test two answer the

following problems show your complete solution in your notebook number one June wanted to know how much ice cream

he got in one scoop the radius of a scoop is 2 in find the volume use 3.14 for pi so what is as in the problem the

volume of one scoop of ice cream what are the given facts Radius 2 in 3.14 for pi what is the formula to be used volume

of a sphere volume equal 4/3 * radius to the 3 power number sentence and final answer so use this formula volume = 4/3

* 3.14 > * the radius 2 so multiply 2 * 2 * 2 = 8 then multiply 3.14 * 8 = 25.12 then multiply 25.12 * 4 / 3 = 33.4

9 cubic in number two find the volume of milk chocolate in a glass with a radius of 5

cm and height of 10 cm what is as in the problem the volume of milk chocolate in a glass what are the given facts radius

equal 5 cm height equal 10 cm 3.14 for pi what is the formula to be used volume of a cylinder volume equals Pi radius

square height number sentence and Final Answer use this formula so 3.14 which is the pi * the radius 5 * height 10 cm

multiply first 5 * 5 = 25 then multiply 3.14 * 25 = 78.5 then multiply by 10 78 8.5 * 10

= 785 cubic cm this is the volume of milk chocolate in a

glass number three calculate the volume of the pyramid in the picture what is the formula to be

used volume of pyramid equal 1/3 * area of Base * height the formula is this volume equal 1/3 base height or volume =

1/3 length * width * height so volume = 1/3 multiply the length and the width which is 4 * 4 and then multiply the

height first multiply 4 * 4 = 16 then multiply 16 * 4 / 3 = 2133 cubic

M number four m has a large plastic cup that he is going to fill with water the plastic cup is in the shape of a cone

with a height of 7 in and a radius of 3 in as shown find the volume of the water in the plastic cone cup so what is the

formula to be used the formula is volume = 1/3 base * height or 1/3 Pi radius square and here is the number sentence

and The Final Answer use this formula 1/3 * 3.14 * 3 * 3 which is the radius * 7 which is the height so 3 * 3 = 9 then

multiply 9 * 7 = 63 then multiply 3.14 * 63 = 19782 divided by 1/3 equal

6594 cub Ines for learning Tas three answer the questions that follow put a check mark

on the space provided copy and answer in your math notebook number one the units for volume

are always is it squared or always cubed what is the correct answer correct the answer is Cube the

units for volume are always cubed number two volume is the amount of space an object takes up is it true or

false very good the correct answer is true calculate for the volume of solid for number three Chona is selling

Pringle chips to raise money for a field trip the container has a diameter of 9 in and a height of 32

in so find the volume of a cylinder and the formula is volume equal Pi radius square height Pi is

3.14 radius is 4.5 multiply by itself and the height is 32 in so multiply the radius by itself 4.5

* 4.5 = 20.25 and then multiply 3.14 * 20.25 = 63. 585

* 32 in = 23472 cubic

in number four a three Tire cake with the same height of 10 in and radius of 12 in 8 in 5 in respectively is to be

delivered to a birthday party how much space does this cake take up use 3.14 for pi so first get the volume 1 3.14 *

the radius 12 in * the height 10 in or multiply the radius by itself 12 * 12 = 144 and then multiply 3.14 * 144 * 10 =

45216 Volume 2 3.14 * 8 8 in which is the radius * 10 which is the height so multiply the

radius by itself 8 * 8 = 64 and then multiply 3.14 * 64 * 10 = 29.6 volume 3

3.14 * 5 which is the radius * 10 which is the height first multiply the radius by itself 5 * 5 = 25 5 and then multiply

all 3.14 * 25 * 10 = 785 and then add the three volumes volume 1 is

45216 plus Volume 2 29.6 + volume 3 785 equal

7,31 2016.2 cubic in for number five as styrofoam model of a volcano is in the shape of a cone the

model has a circular base with a diameter of 48 cm and a height of 12 CM find the volume of Po in the model to

the nearest St use 3.14 for pi use this Formula First multiply the radius by itself 24 * 24 =

576 then multiply 576 * 12 = 6,912 then multiply 3.14 *

6,912 = 21736 divided by 1/3 equal

7,234 56 cubic cm and for learning task 4 solve each of the following problems

draw an illustration of each solid figure described in the problem then write your solution and final answer on

a piece of paper for number one the base of a pyramidal tent is a square the tent is 2

m long and 1 and 1/2 M High how many cubic M of space can it hold inside number two a cone hat has a radius of

1.3 DM and a height of of 4 decim what is its volume number three find the volume of a sphere whose diameter is 234

M and for number four how much space is occupied by a cylindrical capsule with a radius of 10 m and a height of 30 m kids

now it's your turn to answer numbers 1 to 4 so kids do you understand our lesson

for today wow good

job kids I hope you learn a lot from this lesson until our next topic bye-bye kids thanks for watching

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