Question

Find the volume of the hemisphere of radius 3.5 cm.

Answer 1

Hint: Use the formula for calculation of volume of hemisphere which is \[\dfrac{2\pi }{3}{{r}^{3}}\] and substitute the given radius of hemisphere to find the volume.

We have a hemisphere whose radius is equal to \[3.5\] cm. We have to calculate the volume of the given hemisphere.
We know that if the radius of the hemisphere is \[r\] units, then the volume of hemisphere is given by \[\dfrac{2\pi }{3}{{r}^{3}}\] units. Radius is the distance from the centre point of a hemisphere to the circumference, an outside ring. The radius is always half of the diameter.
Substituting \[r=3.5\] in the above formula, we get volume of hemisphere \[=\dfrac{2\pi }{3}{{\left( 3.5 \right)}^{3}}\].
Substituting \[\pi =\dfrac{22}{7}\] in the above formula, we get volume of hemisphere \[=\dfrac{2\pi }{3}{{\left( 3.5 \right)}^{3}}=\dfrac{2}{3}\times \dfrac{22}{7}\times {{\left( 3.5 \right)}^{3}}=\dfrac{2}{3}\times \dfrac{22}{7}\times \dfrac{35}{10}\times \dfrac{35}{10}\times \dfrac{35}{10}\].
Cancelling out like terms from numerator and denominator, we get volume of hemisphere \[=\dfrac{22}{3}\times \dfrac{35}{10}\times \dfrac{35}{10}=89.834c{{m}^{3}}\].
Hence, the volume of the hemisphere of radius \[3.5\] cm is equal to \[89.834c{{m}^{3}}\].
A hemisphere is a \[3-\] dimensional object that is half of a sphere. A sphere is defined as a set of points in \[3-\] dimension and all the points lying on the surface are equidistant from the centre. When a plane cuts across the sphere at the centre or equal parts, it forms a hemisphere. In general, a sphere makes exactly two hemispheres.
Volume is the amount of space inside of an object or the space that an object occupies.

Note: One must be careful about using the formula for calculating the volume of the hemisphere. The volume of the hemisphere is not the same as the volume of the sphere. Its volume is half of the volume of the sphere of the same radius.