- Naturvetenskapsprogrammet (före 2011) Årskurs 2
- Matematik D
Matte D uppgift 7 a
Uppgiften ger en förklaring på hur du räknar ut maximalvolymen av en kon
a) The task is to make a cone of a circle with so big volume as possible. In the figure below you can see a sketch of how you should do it. So the task is to figure out the angle v of a circle and then what the cone with the maximum volume would be.
b) Now you should make two cones, one of the piece that I cut off and one of the one who's left. But now you should decide the angle so the both cones together make the maximum volume.
c) Make the two cones out of paper with a radius of 10 cm.
the formula I'm going to use in this calculation. But first I need to know the circumference.
will give us the circumference and if we
divide that with 2π
we will get the radius of the base of the cone, which is
Then we can calculate the height of the cone, with help of Pythagoras.
r² = (rx)²+h²
r²-r²x² = h²
r²(1-x²) = h²
r√(1-x²) = h
And from that we can now start on calculate the maximum volume. So we are getting back at the way I started it with the formula of how you calculate the volume of á cone... Köp tillgång för att läsa mer