# Right-angled triangle turned around height to make cone

A right angled triangle, having base 6.3 m and height equal to 10 cm, is turned around the height. Find the volume of the cone thus formed. Also find the surface area.

I can solve this question there is only one hinderance that I need to overcome. Please help me to sort this out.

My query : When right angled triangle is turned around its height,

the height of the cone= height of the right angled triangle.

the base of the cone=?

slant height= hypotenuse of the right angled triangle.

The base of the cone is a circle with radius equal to the base of right triangle. To help you imagine better, you may first consider a square which is revolved around one of its sides. This will give a circular cylinder. Now, you can see why the base of the cone is a circle!

• It will be helpful if you can explain, why so? – Vibhu Oct 15 '15 at 9:28
• See the edit. :) – H. R. Oct 15 '15 at 9:32
• circular base, so it should be 2πr=base of the right angled triangle? – Vibhu Oct 15 '15 at 9:42
• Sorry, I didn't get you. Are you now OK with the base of the cone being a circle? – H. R. Oct 15 '15 at 9:44
• The radius of this circular base of the cone is equal to the base of the right triangle. – H. R. Oct 15 '15 at 9:45

Your cone will have a circular base, where the radius of the circle will be the width of your triangle.

• circular base, so it should be 2πr=base of the right angled triangle? – Vibhu Oct 15 '15 at 9:27
• Mark a paper model and post a photo, it may become clearer. Is it 6.3 m or cm? – Narasimham Mar 12 '16 at 15:18

Assume triangle ABC with AB as height and AC as base Now you have to see that it's not transformation of 2D to 3D(Eg: cylinder from Square or rectangle)

Its like you holding triangle in vertical direction ( B at top, A on ground ) and then make a full 360• rotation around height holding C (Keep AC straight) (To rotate full triangle)

Now you see

Height of Triangle = height of cone ;

Base of Triangle = radius of cone ;

Use formulas to find required values

• I don't think you've added anything to the existing Answers, although you did address the issue of how the base of the cone relates to the base of the triangle. In the future please look over existing Answers to months-old Questions to check if you are really adding new information. If so, be sure to highlight that for your Readers. – hardmath Mar 12 '16 at 15:17