Question

A right circular cone us placed inverted and filled up to half of height which contains 20ml water find capacity of cone

Answer 1

Let h be the height of the right circular cone and R be the radius.

Let r(x) be the radius at a cross-section of the cone where we assume x=0 is at the bottom. So, r(0)=0,r(h)=R. Thus, r(x)=Rhx.

Then, the volume of the whole cone is
V=13πR2h.
Initially, the cone is only filled up to half its vertical height, so the volume of the liquid is
V0=13π(r(h2))2h=13π(R2)2h
because it is only filled half.

Now, when you invert the cone, you want to find that height x for which
V−13π(r(x))2h=V0.
That leads to 1−(xh)2=14 and x=3√2h.

Remember x=0 is the bottom of the original cone. Thus, your answer will be that the inverted cone is filled up to a height of 1−3√2 of the total vertical height.

hope it helps

Answer 2

Answer: 160 ml

Explanation: The right angled cone is inverted. As we go down, the radius and the height decreases equally.

Suppose Base radius is R and total height of cone is H. At half cone, height is h and radius is r. At half height h = H/2.

As the cone is right angled, the ratio of

H/h = R/r.

substituting h=H/2 in above equation we get r =R/2.

Refer the image for proper answer