Cone volume and side are from axial section area

[Merkatih]

Hi smart people!

i have been on this exercise for 2 hours and can’t seem to get the right answer. Please help or just have fun buy figuring it out.

there is a cone whose axial section is a right triangle and the triangle’s area is 9sqm.

what it the side area and volume of that cone?

thanks in advance

 

[Deleted member 4993]

Hi smart people!

i have been on this exercise for 2 hours and can’t seem to get the right answer. Please help or just have fun buy figuring it out.

there is a cone whose axial section is a right triangle and the triangle’s area is 9sqm.

what it the side area and volume of that cone?

thanks in advance

As posted the above problem cannot be solved. Post an image of the given problem.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[Merkatih]

As posted the above problem cannot be solved. Post an image of the given problem.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

Unfortunately the problem is in Estonian hence posting a picture about it won’t helo. I have translated all given information.

i assumed the triangle would be equilateral which would mean that the sides would be 3m, 3m and 3√2, hence radius 3√2/2 but that didn’t give the right answer.

according to the book the side area should be 9√2pi sqm2 and volume 9pi m3

 

[Dr.Peterson]

there is a cone whose axial section is a right triangle and the triangle’s area is 9sqm.

what it the side area and volume of that cone?

Is it a right circular cone? Or something else (like an oblique elliptical cone)?

From the area of the section, can you find the height and diameter of the cone?

 

[Merkatih]

Is it a right circular cone? Or something else (like an oblique elliptical cone)?

From the area of the section, can you find the height and diameter of the cone?

It doesn’t specify..


i assumed it would be right circular cone and the triangle would be equilateral which would mean that the sides would be 3m, 3m and 3√2, hence radius 3√2/2 but that didn’t give the right answer.

according to the book the side area should be 9√2pi sqm2 and volume 9pi m3

 

[Dr.Peterson]

It doesn’t specify..


i assumed it would be right circular cone and the triangle would be equilateral which would mean that the sides would be 3m, 3m and 3√2, hence radius 3√2/2 but that didn’t give the right answer.

according to the book the side area should be 9√2pi sqm2 and volume 9pi m3

Yes, we can probably assume it's a right circular cone; but the triangle can't be equilateral if it has a 90 degree angle.

Surely (from your numbers) you meant a right isosceles triangle?

The area of the triangle you describe is not 9 m^2! Think just a bit more. ("Sqm2" is not a valid unit.)

Then please show us your actual work, rather than just a general description, if you still get a wrong answer.

(But thanks for giving the answer you are comparing yours to -- sometimes the problem is that the given answer is wrong, but these answers are indeed correct.)

 

[Merkatih]

Yes, we can probably assume it's a right circular cone; but the triangle can't be equilateral if it has a 90 degree angle.

Surely (from your numbers) you meant a right isosceles triangle?

The area of the triangle you describe is not 9 m^2! Think just a bit more. ("Sqm2" is not a valid unit.)

Then please show us your actual work, rather than just a general description, if you still get a wrong answer.

(But thanks for giving the answer you are comparing yours to -- sometimes the problem is that the given answer is wrong, but these answers are indeed correct.)

So I found my mistake which was very primitive - triangle area formula.

thanks for help