A hollow cylindrical glass with a base radius $R$ is fixed on a horizontal table surface. One of the following bodies — either a sphere or a cone suspended by the center of its base — is lowered into it on a thread.

Then, at time $t=0$, water begins to be poured into the glass at a constant volumetric flow rate $\mu = 1.00~\text{cm}^3/\text{s}$. During the experiment, the dependence of the liquid level height $h$ in the glass on time $t$ was measured. The obtained results are given in the table “data.xlsx”.

A0 If you use an Excel table to solve the problem, submit it. All actions performed in the table must be described in the solution.

A1  ^1.00 Which body is lowered into the glass?

A2  ^1.50 Does the body touch the bottom? If there is a gap between the lower edge and the bottom, what is it equal to?

A3  ^1.00 The radius of the glass base is $R$.

A4  ^4.00 The geometric dimension $a$ of the body lowered in the glass: either the radius of the sphere or the radius of the base of the cone.

A5  ^1.00 The moment in time $t_0$ when the thread begins to go slack.

A6  ^1.50 Plot a graph of the buoyancy force acting on the body as a function of time.

Density of water $\rho_0 = 1.00~\mathrm{g}/\mathrm{cm}^3$, acceleration due to the gravity $g = 9.8~\mathrm{m}/\mathrm{s}^2$.