Question

What is the total surface area of the hemisphere?
(A) \[4\pi {r^2}\]
(B) \[3\pi {r^2}\]
(C) \[\dfrac{2}{3}\pi {r^2}\]
(D) \[\dfrac{4}{3}\pi {r^2}\]

Answer 1

Hint: The hemisphere is the half of the sphere. It consists of two surfaces. One is the outer surface which is called the curved surface area and the other one which is present in the bottom which is called the flat surface area. If we add these two surfaces we will get the total surface area of the hemisphere.

Complete step by step solution:
From the term hemisphere, we can say that it is half of the sphere. The total surface area of the hemisphere will be the combination of the curved surface area and the flat surface area.

First, let us find the curved surface area.
Curved surface area is half of the surface area of the sphere.
Curved surface area =\[\dfrac{1}{2} \times \]surface area of the sphere ------ (1)
We know that the surface area of the sphere is\[4\pi {r^2}\] square units
Substituting in (1)
=\[\dfrac{1}{2} \times 4\pi {r^2}\]
 =\[2\pi {r^2}\]
The curved surface area of the sphere is \[2\pi {r^2}\] square units ------ (2)
Next, we have to find the flat surface area. This portion is the base of the hemisphere. It looks exactly like a circle. So we can use the area of the circle formula.
The area of the circle =\[\pi {r^2}\] square units ------ (3)
Now if we add equations (2) and (3) we get the total surface area of the hemisphere.
The total surface area of the hemisphere
 \[ = 2\pi {r^2} + \pi {r^2}\]
 \[ = 3\pi {r^2}\]Square units
Therefore the correct option is B \[ = 3\pi {r^2}\] square units.

Note:
The area is usually measured in square units. Is a constant whose value is 3.14.r is the radius of the hemisphere.
Note how the surface area of a sphere is divided by two before being added to the circle area.