Question

Find the total surface area of a hemisphere of radius 10cm.

Answer 1

Hint: A hemisphere is half of a sphere. So the total surface area of a hemisphere is half the surface area of a sphere plus the area of the base circle. Total surface area of a hemisphere is $ \dfrac{1}{2}\left( {4\pi {r^2}} \right) + \left( {\pi {r^2}} \right) $ which is half the total surface area of a sphere and area of the base.

Complete step-by-step answer:

A hemisphere is defined as a three-dimensional shape that's half of a sphere with one flat, circular side. A hemisphere is obtained when we cut the sphere into two equal halves. The total surface area of the hemisphere will be equal to the sum of its curved surface area and the base area of the hemisphere. The base is in circular shape here. We can find various real-life examples of the hemispheres such as our planet Earth can be divided into two segments which are southern & northern hemispheres. Curved or Lateral surface area of a hemisphere is $ 2\pi {r^2} $ .
Total surface area of a hemisphere is $ 3\pi {r^2} $ where ‘r’ is the radius of the hemisphere and $ '\pi '\ $ is equal to 22/7 or 3.14.
We are given that the radius of the hemisphere is 10cm.
r=10cm.
Total surface area of the given hemisphere = $ 3 \times \pi \times r \times r $
 $
   = 3 \times \dfrac{{22}}{7} \times 10 \times 10 \\
   = \dfrac{{66 \times 100}}{7} \\
   = \dfrac{{6600}}{7} \\
   = 942.857c{m^2} \\
  $
Therefore, the total surface area of a hemisphere with radius 10cm is 942.857 square centimeters.

Note: The Hemispheres can either be of a solid type or can be hollow. Total Surface area of a hollow hemisphere is different from the total surface area of a solid hemisphere. Do not confuse a solid hemisphere with a hollow hemisphere.