A sphere of radius 3.5 cm and mass 250 gm floats in a liquid at `20^(@)C`. As the temperature is raised, the sphere just being to sink at a temperature of `35^(@)C`. If the density of liquid at `0^(@)C` is `1.527gm//cm^(3)` find the coefficient of cubical expansion of the liquid. Neglect expansion of the sphere.

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Calculate the Density of the Sphere
The density of the sphere (\( \rho_s \)) can be calculated using the formula:
\[ \rho_s = \frac{m}{V} \]
where \( m \) is the mass of the sphere and \( V \) is its volume. The volume \( V \) of a sphere is given by:
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