0
$\begingroup$

Find the volume of a right circular cone formed by joining the edges of a sector of a circle of radius r cm where the sector angle is 90 degrees.

I am not able to visualize this whole scenario. How can we do this one? What will be the radius and what will be the height of the cone after joining the edges? I will be really thankful if someone can just help me out with its figure

$\endgroup$
0
$\begingroup$

If I read this right, this can be visualized as follows: (1) Draw a circle of radius r on a piece of paper; (2) Cut out the circle; (3) Cut the circle in half along a diameter; (4) Cut one of the half-circles in half along a radius; (5) Take one of the quarter-circles and roll it up, joining the two radius-edges. (6) You now have a cone - calculate its volume.

$\endgroup$
0
$\begingroup$

You can use the circumference of the circle to get the circumference of the base of the cone. This will give you the radius of the base of the cone. Additionally, you have the slant height from the original radius - from these two, you can get the height of the cone.

$\endgroup$
  • $\begingroup$ I did not understand @S.Ong $\endgroup$ – EmilySekuz Aug 2 '17 at 20:28
  • $\begingroup$ Based on the dimensions of the original circle, you can find the length of the "round" edge of the sector. This edge will become the edge of the base of your cone. Then you can find its radius. For the height of the cone, imagine taking a vertical cross-section; you'll be left with an isoceles triangle. You should be able to use Pythagoras to solve for its height (try drawing a diagram!) $\endgroup$ – platty Aug 2 '17 at 20:34
  • $\begingroup$ I am not able to do it. Never mind @S.Ong $\endgroup$ – EmilySekuz Aug 2 '17 at 20:41
  • $\begingroup$ Don't give up yet! Let's take this one step at a time; what is the circumference of your original circle? Then what is the length of the curved portion of the sector? $\endgroup$ – platty Aug 2 '17 at 20:43
  • $\begingroup$ I assumed the base of the coin as 'a'. Now If I will join four edges of a sector then I will get circumference of cone. @S.Ong $\endgroup$ – EmilySekuz Aug 2 '17 at 20:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.