Question

A cone is filled with water up to a certain height such that the height of the cone left unfilled is 8 cm. On inverting the same cone, the height of cone left unfilled is 2cm. Calculate the height of the cone

Answer 1

Answer:

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.

Answer 2

Answer:

please follow this

Step-by-step explanation:

please mark me as brainliest