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Surface Area of Sphere and Hemisphere




Here we will discuss surface area of sphere and hemisphere

Sphere is nothing but a any type of ball. As it is in circular shape so it has diameter and radius.

Diameter : A line segment through the center of a sphere and with the end points on its boundary is called its diameter.


OP is the radius of the sphere.

Section of a spherical shape by a plane is called the Hemisphere.

Formulas for surface area of sphere -hemisphere :
Sphere :
Surface area (TSA) = CSA = 4πr2
Hemisphere :
Curved surface area(CSA) = 2 π r2
Total surface area = TSA = 3 π r2

Some solved examples on surface area of sphere - hemisphere

1) The radius of hemispherical balloon increase from 7 cm to 14 cm as air is being pumped into it. Find the ratios of the surface areas of the balloon in two cases.
Solution :
For 1st hemisphere, r = 7 cm
TSA -1 = 3 π r
2
⇒ = 3 x π x 7
2
TSA-1 3 π x 72 1
-------- = --------- = ----
TSA -2 3π x 142 4
⇒ S 1 : S 2
= 1 : 4
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2) Show that the surface area of sphere is same as that of the lateral surface area of a cylinder that just encloses the sphere.
Solution :

Total surface area of sphere = 4 π r
2 ------(1)
The radius and height of the cylinder that just encloses the sphere of radius r and 2r respectively.
∴ CSA of cylinder = 2 π r h
⇒ = 2 π r x 2r
∴ CSA of cylinder = 4 π r
2 ----(2)
∴ From (1) and (2)
Surface area of sphere is same as that of the lateral surface area of a cylinder that just encloses the sphere.

Surface Area :

Surface Area of Cube
Surface Area of Rectangular Prism(Cuboid)
Surface Area of Cylinder
Surface Area of Cone
Surface Area of Sphere and Hemisphere
Surface Area of Prism
Surface Area of Pyramid

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