Total Surface Area of Hemisphere with Formula
Total Surface Area of Hemisphere is the sum of its curved surface area and circular base area. For radius r, the formula is 3πr² square units. This page explains the formula, its diameter form, the difference between curved and total surface area, and solved numerical examples for quantitative aptitude.
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What Is the Total Surface Area of a Hemisphere?
The curved surface area of a hemisphere is 2πr², while its circular base has area πr². Therefore, TSA = 2πr² + πr² = 3πr² square units. If the diameter is d, then r = d/2 and TSA = 3πd²/4.
Total Surface Area of Hemisphere Video Lessons
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Sphere and Hemisphere: Volume and Surface Area
Learn the formulas and methods to calculate the volume and surface area of spheres and hemispheres, including how to apply them to quantitative aptitude problems.
Total Surface Area of Hemisphere Formula & Tricks
Important Formulas
Use this when the radius r of the hemisphere is given. The result is expressed in square units.
Use d as the diameter. This follows from substituting r = d/2 into 3πr².
This includes only the curved half-spherical surface and excludes the circular base.
The base of a hemisphere is a circle with radius r.
Quick Tricks
The total surface area is three-halves of the curved surface area because 3πr² ÷ 2πr² = 3/2.
When the diameter is given, avoid finding the radius separately by using TSA = 3πd²/4.
Total Surface Area of Hemisphere Concepts
Curved Surface Area Versus Total Surface Area
For radius r, CSA = 2πr² and TSA = 3πr². The difference between them is exactly the base area πr². A closed solid hemisphere has a base, so its total surface area includes this circular region.
Calculating TSA When Radius Is Given
Apply TSA = 3πr². Use π = 22/7 when the radius is a multiple of 7, and use π = 3.14 when the question specifies it or when an approximate answer is required.
Calculating TSA When Diameter Is Given
First identify whether the given measurement is a diameter or radius. For diameter d, TSA = 3π(d/2)² = 3πd²/4. The answer is always in square units.
Finding Radius from Total Surface Area
Start with A = 3πr². Divide by 3π and take the positive square root because a length cannot be negative. If the area is given in square centimetres, the radius is obtained in centimetres.
Total Surface Area of Hemisphere Visual Guide
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Hemisphere with radius and circular base
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Total Surface Area of Hemisphere: Revision Points
Use these formulas and rules for quick revision.
- TSA of a solid hemisphere = 3πr².
- Curved surface area = 2πr².
- Circular base area = πr².
- TSA = CSA + base area.
- If diameter is d, TSA = 3πd²/4.
- For a given TSA A, radius r = √(A/(3π)).
- Area is measured in square units, such as cm² or m².
- Use the positive value of radius because radius represents length.
Total Surface Area of Hemisphere FAQs
What is the total surface area of a hemisphere formula?
The formula is TSA = 3πr², where r is the radius. It includes the curved surface and the circular base.
What is the total surface area of a hemisphere in terms of diameter?
If d is the diameter, TSA = 3πd²/4.
What is the total surface area of a hemisphere with radius 7 cm?
Using π = 22/7, TSA = 3 × 22/7 × 7² = 462 cm².
What is the difference between curved and total surface area of a hemisphere?
CSA = 2πr² includes only the curved surface. TSA = 3πr² includes the curved surface and the circular base.
What is the total surface area of a hemisphere with diameter 14 cm?
TSA = 3πd²/4 = 3 × 22/7 × 14²/4 = 462 cm².
If the total surface area of a hemisphere is 75π cm², what is its radius?
Using 3πr² = 75π, r² = 25, so the radius is 5 cm.