Give a sphere, a cone is constructed so that cone and the sphere have the same volume but the total surface area of the cone is k times that of the sphere where K is determined so that there is a unique cone satisfying this property . Then k = ? a) 1 b) ∛2 c) √3 d) √2
Answers
Answered by
1
We use the formulae to get the volume of the sphere and also the volume of the cone.
Since the volumes are equal we equate them so that we get the height of the cone.
Once we get the height of the cone which is 4r,we use Pythagoras theorem to get the l of the cone which it is the hypotenuse.
We then use the formulaes for getting the SA of the cone and the sphere.
We then equate them using the scalar K so that we get its value.
When we solve this, we get the value of K as 1.2808
Find working in the image below.
Since the volumes are equal we equate them so that we get the height of the cone.
Once we get the height of the cone which is 4r,we use Pythagoras theorem to get the l of the cone which it is the hypotenuse.
We then use the formulaes for getting the SA of the cone and the sphere.
We then equate them using the scalar K so that we get its value.
When we solve this, we get the value of K as 1.2808
Find working in the image below.
Attachments:
Similar questions