Real-World Problems Using Volume of a Cylinder Formula

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hey there everyone and welcome back to

mashup math my name is Anthony and thank

you for joining me on this mini lesson

just go ahead and check it out hey

everyone thank you again for stopping by

and joining me on this practice problem

where we are going to gain some

experience using formulas and some

algebra skills to solve problems so

let's go ahead and model this scenario

we have a cylinder that has a diameter

of 10 centimeters now we know that half

of a diameter is a radius so half of 10

is 5 so in this case the cylinder has a

radius of 5 centimeters now the next

important piece of information that we

are given is that the cylinder has a

volume of 225 PI cubic centimeters so we

can represent this by writing that V the

volume is equal to 225 pi and what we

are actually trying to figure out in

this problem is the height of the

cylinder in centimeters since we don't

actually know how tall this cylinder is

so what we will be solving for is the

value of H the height of the cylinder in

centimeters now you probably already

have some experience finding the volume

of a cylinder by plugging the values of

the radius and the height into the

formula for finding the volume of a

cylinder but in this case we don't know

the value of H so we can't use the

formula directly in ways that we're used

to however we are still going to use the

formula for finding the volume of a

cylinder to find the solution to this

problem and we know that the formula for

the volume of a cylinder

is equal to

pi multiplied by the radius squared

multiplied by the height and since we

were already given the volume of this

cylinder we know that this product will

be equal to 225 pi now all that we have

to do is use some algebra skills to find

the value of H now we should notice that

we have a PI on both sides of the equal

sign now we can actually divide by PI on

both sides to effectively cancel these

out from either side of the equation

cool now since we know that the radius

of the cylinder is 5 we can substitute

the value of R with 5 and we know that 5

squared is equal to 25

so now we are left with 25 times the

height is equal to 225 and remember

we're solving for H here we're trying to

get H by itself and find out what value

it represents we can do that by

performing inverse operations the

opposite of multiplying by 25 is to

divide by 25 on both sides of the equal

sign that will cancel out on the left

side of the equal sign on the right side

225 divided by 25 is equal to 9 and we

can conclude that the height of this

cylinder is equal to 9 centimeters so if

this is your first time solving a

problem like this it's a good idea to go

back and go through it a few more times

they can be a little bit tricky but if

you put in the effort and practice a

little bit they do get a lot easier just

remember that when you're using formulas

you can use them in a variety of

different ways and that it's also very

important to model problems like this by

drawing your own picture so that you can

better understand what's going on and

find the solution so that's it for this

problem thank you again so much for

stopping by and I will see you all next

time bye alright so that's it for this

lesson thank you again for stopping by I

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