UPSKILL MATH PLUS

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Learn more### Theory:

The volume of the solid formed by combining two more solids is obtained by simply calculating the volume of the individual solids and adding them.

Suppose a solid is in the form of a cone surmounted on a hemisphere, then its volume is given by the sum of the volume of the cone and the hemisphere.

Let us discuss an example to understand the concept better.

Example:

The interior of the glass is in the form of a cylinder surmounted on a hemisphere has a uniform radius of \(4\) \(cm\) and the height of the cylindrical part is \(7\) \(cm\). Find the capacity of the glass.

**Solution:**

**The volume of the glass**\(=\) Volume of the hemisphere \(+\) Volume of the cylinder

**Volume of the glass**\(=\) \(\frac{2}{3} \pi r^3 \) \(+\) \(\pi r^2 h\)

\(=\) \(\left[\frac{2}{3} \times \frac{22}{7} \times (4)^3\right]\) \(+\) \(\left[\frac{22}{7} \times (4^2) \times 7 \right]\)

\(=\) \(\left[\frac{2}{3} \times \frac{22}{7} \times 64\right]\) \(+\) \(\left[\frac{22}{7} \times 16 \times 7 \right]\)

\(=\) \(134.1\) \(+\) \(352\)

\(=\) \(486.1\) \(cm^3\)

Therefore, the capacity of the glass is \(486.1\) \(cm^3\).