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 r²
⇒ = 3 x π x 7²

TSA-1 3 π x 72 1 -------- = --------- = ---- TSA -2 3π x 142 4

⇒ S₁ : S₂ = 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 r² ------(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 r² ----(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.

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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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