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 = 4πr^{2} Hemisphere :
Curved surface area(CSA) = 2 π r^{2} Total surface area = TSA = 3 π r^{2}
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 7^{2} 1 -------- = --------- = ---- TSA -2 3π x 14^{2} 4
⇒ S_{1} : S_{2} = 1 : 4
_________________________________________________________________
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 :