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Surface Area of Hemisphere: Formula, Calculate TSA, CSA, LSA of Hemisphere

Surface Area of Hemisphere

A Hemisphere is a half sphere, one half of a sphere or globe that is divided by a plane passing through its center. To calculate the Surface Area Of Hemisphere a particular Formula is used. The Formulas of Surface Area of Hemisphere includes TSA, CSA, LSA.

Here on this page of recruitmentresult.com we have stated the Total Surface Area Of Hemisphere, Curved Surface Area Of Hemisphere along with Lateral Surface Area Of Hemisphere and Volume. You are advised to go through the information now…

Surface Area of Hemisphere

Surface Area Of Hemisphere

Curved Surface Area of Hemisphere

Since a hemisphere is the half of a sphere, the curved surface of a hemisphere is also half of that of a sphere.

⇒ CSA⇒ CSA of hemisphere = 1/2 (Surface area of sphere)

or Curved Surface Area of a Hemisphere 2πrsquare unit

Example:

Find the total surface area of the hemisphere which is of radius equal to 11 cm.

Solution:

The radius of the hemisphere, r = 11 cm.

We know, total surface area of a hemisphere is given by 3 ππ r2 square units.

Therefore,

Total Surface Area = 3 * 3.14 * 112

= 3 * 3.14 * 11 * 11

Total Surface Area = 1139.82 cm2

Get Here Formula: Surface Area of Sphere

Lateral Surface Area Of Hemisphere

Lateral Surface Area Of A Hemisphere Formula =
LSA of hemisphere = 4 π r²

Example:

Question: If the lateral surface area of the solid hemisphere is 2772 sq.cm, then find its radius.

Solution:

Lateral surface area of hemisphere = 2772 cm²

 2 Π r²  = 2772 ==> 2 x (22/7) x r²  = 2772

r²  = 2772  x (1/2) x (7/22) ==> r²  = 441 ==>  r = 21

Radius of hemisphere = 21 cm

Question: Find the LSA of a hollow hemisphere whose outer and inner radii are 4.2 cm and 2.1 cm respectively.

Solution:

Inner radius (r) = 2.1 cm

Outer radius (R) = 4.2 cm

In this we will use the Formula Of Lateral Surface Area Of Hemisphere

LSA of hollow hemisphere = 2Π (R² + r²)

= 2 x Π x [(4.2)² + (2.1)²] ==> 2 x Π x (17.64 + 4.41)

= 2 x Π x (22.05) ==>  44.1 Π cm²

LSA of hollow hemisphere = 44.1 Π cm²

Get Properties, Theorems & Derivation: Area of Trapezoid

Total Surface Area of a Hemisphere

Total surface area is the sum of the curved surface area plus the area of base surfaces.

TSA = Curved surface area + base area (base is circular)

= 2πr2 + πr2 =3πr2

where, r is radius.

Formula for Total Surface Area of Hemisphere = 3πr2 square units

Example:

The radius of the hemisphere is 3.5 cm. find its total surface area.

Now here r = 3.5

According to the Total Surface Area Of Solid Hemisphere TSA = 3πr2

Putting the values = 3* 3.14 *(3.5)2

Hence the Total Surface Area Of A Hemisphere is= 115.395 square units

Check Out: Area of Semicircle Formula

Total Surface Area Of Hollow Hemisphere

Total Surface Area Of Hollow Hemisphere

Total Surface Area Of Hemisphere Formula (Hollow) = Outer Surface Area + Inner Surface Area + Area Of Ring

Example:

Imagine a hollowed hemisphere. The radius out the outer sphere is 1.25cm. The diameter of the inner sphere is 1.86 cm. What is the total surface area of the entire figure?

Surface area of a hemisphere is: 2πr2

This hemisphere is hollow.  It has a total surface area of:

outer surface area + inner surface area +area of ring

 2π(1.25)2   + 2π(1.86/2)2  + (π(1.25)2  –  π(1.86/2)2  )

 3π(1.25)2 +π(1.86/2)2

 3π(1.25)2 +  π(0.93)2

14.71875 + 2.715786

17.43454

17.43 cm2 (rounded)

Get Methods with Examples: Area of Ellipse Formula

Volume of Hemisphere

Volume of Hemisphere = (2/3)πr³

Example:

Find the Volume of the hemisphere which is of radius equal to 11 cm.

Since according to the Formula of Volume of Hemisphere = V= (2/3)πr³

Putting the values = (2/3) * (3.14) * (11)3

Volume of Hemisphere = 2786.23

Get Maths Vedic/Basic Formulas Free List: Maths Formulas

A Combined Example:

Find the volume, curved surface and total surface area of a hemisphere with the given radius 2.

Step 1: Find the volume.
Volume = (2/3)πr³ = (2/3) * 3.14 * 2³ = 0.67 * 3.14 * 8 = 16.8304

Step 2: Find the curved surface area (CSA).
Curved Surface Area(CSA) = 2πr² = 2 * 3.14 * 2² = 6.28 * 4= 25.12

Step 3: Find the total surface area (CSA).
Total Surface Area(TSA) = 3πr² = 3 * 3.14 * 2² = 9.42 * 4 = 37.68

We hope with the help of information given here on this page it will become easier for you all to understand the concept of Formula of Surface Ares of Hemisphere.  To get more related updates keep visiting our pages.

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