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"hello students welcome to lido q a video session i am seth your math tutor and question for today is find the volume of the right circular cone with radius 6 centimeter height 7 centimeter radius 3.5 centimeter height 12 centimeter height 21 centimeter slant height 28 centimeter so these three questions we need to solve here we'll take one partition and solve one by one the very first question here is given that radius the radius that is given is 6 centimeter radius of right circular cone that is r and that is equal to 6 centimeter now height is given that is height of right circular cone h is equal to 7 centimeter what you need to do over here is just apply the formula for volume of a right circular cone so volume of a right circular cone is equal to 1 by 3 pi r square h so that is equal to v that is 1 by 3 into 3.14 into the radius is 6 square that is radius square into height that is 7 solving this you will get 264 centimeter cube as your volume of the right circular cone now the second thing over here you need to find is again the volume of the right circular cone from the given data of radius and height so radius here that is r given that is 3.5 centimeter and height h that is 12 centimeter again you apply the same formula that is volume of a right circular cone one by three pi r square h 1 by 3 into 3.14 into radius square is 3.5 square into 12 square so that is equal to here 154 centimeter cube so your volume of a right circular cone over here is 154 centimeter cube now in third question you have been given height and slant height for right circular cone height is 21 centimeter and your slant height let us consider it as letter l that is 28 centimeter the very first thing you need to find here is the radius of right circular cone because in the formula for the volume of the right circular cone we have one term containing radius that is 1 by 3 pi r square into h so here you need to first of all find the radius of the right circular cone so radius of the right circular cone can be given by r square plus or you can write directly h square is equal to l square that means r square is equal to l square minus h square your slant height is 28 centimeters or 28 square minus h square that is 21 square so your r square comes out to be 49 into 7 so here you can write it like this that r is equal to 7 root 7 once you found this r then you have formula for the volume of the right circular cone one by three pi r square h that is 1 by 3 into 3.14 into radius square that is 7 root 7 square into 21 square 1 by 3 into one four into seven if you calculate this then you can get an answer like this around seven five four six seven five four six and the unit is centimeter square so a volume of the right circular cone for this will be seven five four six centimeter square sorry it is a cube because volume is there so here q your final answer for this again i'm repeating that is 7546 centimeter cube so this is our solution for each of these given questions if you have any doubt you can post it in our comment section and subscribe to our channel for more such interesting questions thank you for watching "
Solution
Transcript
"hello students welcome to lido q a video session i am seth your math tutor and question for today is find the volume of the right circular cone with radius 6 centimeter height 7 centimeter radius 3.5 centimeter height 12 centimeter height 21 centimeter slant height 28 centimeter so these three questions we need to solve here we'll take one partition and solve one by one the very first question here is given that radius the radius that is given is 6 centimeter radius of right circular cone that is r and that is equal to 6 centimeter now height is given that is height of right circular cone h is equal to 7 centimeter what you need to do over here is just apply the formula for volume of a right circular cone so volume of a right circular cone is equal to 1 by 3 pi r square h so that is equal to v that is 1 by 3 into 3.14 into the radius is 6 square that is radius square into height that is 7 solving this you will get 264 centimeter cube as your volume of the right circular cone now the second thing over here you need to find is again the volume of the right circular cone from the given data of radius and height so radius here that is r given that is 3.5 centimeter and height h that is 12 centimeter again you apply the same formula that is volume of a right circular cone one by three pi r square h 1 by 3 into 3.14 into radius square is 3.5 square into 12 square so that is equal to here 154 centimeter cube so your volume of a right circular cone over here is 154 centimeter cube now in third question you have been given height and slant height for right circular cone height is 21 centimeter and your slant height let us consider it as letter l that is 28 centimeter the very first thing you need to find here is the radius of right circular cone because in the formula for the volume of the right circular cone we have one term containing radius that is 1 by 3 pi r square into h so here you need to first of all find the radius of the right circular cone so radius of the right circular cone can be given by r square plus or you can write directly h square is equal to l square that means r square is equal to l square minus h square your slant height is 28 centimeters or 28 square minus h square that is 21 square so your r square comes out to be 49 into 7 so here you can write it like this that r is equal to 7 root 7 once you found this r then you have formula for the volume of the right circular cone one by three pi r square h that is 1 by 3 into 3.14 into radius square that is 7 root 7 square into 21 square 1 by 3 into one four into seven if you calculate this then you can get an answer like this around seven five four six seven five four six and the unit is centimeter square so a volume of the right circular cone for this will be seven five four six centimeter square sorry it is a cube because volume is there so here q your final answer for this again i'm repeating that is 7546 centimeter cube so this is our solution for each of these given questions if you have any doubt you can post it in our comment section and subscribe to our channel for more such interesting questions thank you for watching "
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