Curved Surface Area of Hemisphere with Examples

Curved Surface Area of Hemisphere is the area of only the rounded surface of a hemisphere, excluding its circular base. Its formula is 2πr², where r is the radius. This page explains the formula, diameter-based calculation, unit conversion, solved examples and common curved surface area of hemisphere questions.

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What is the Curved Surface Area of a Hemisphere?

The curved surface area of a hemisphere is the area of its half-spherical surface, excluding the flat circular base. It is calculated using CSA = 2πr².

A hemisphere is half of a sphere. Since the surface area of a sphere is 4πr², the curved surface area of a hemisphere is half of it: ½ × 4πr² = 2πr². Here, r is the radius and the answer is expressed in square units. For r = 7 cm, CSA = 2 × 22/7 × 7² = 308 cm².

Curved Surface Area of Hemisphere Video Lessons

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Sphere and Hemisphere: Volume and Surface Area

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Curved Surface Area of Hemisphere Formula & Tricks

Important Formulas

Curved surface area using radius
CSA = 2πr²

Use this formula when the radius r of the hemisphere is given.

Curved surface area using diameter
CSA = πd²/2

Since r = d/2, substituting into 2πr² gives CSA = πd²/2.

Total surface area of a hemisphere
TSA = 3πr²

Total surface area includes the curved surface and the circular base: 2πr² + πr² = 3πr².

Quick Tricks

Use the diameter form directly

When diameter is given, avoid finding the radius separately. Apply CSA = πd²/2.

Example: For d = 14 cm, CSA = π × 14²/2 = 98π = 308 cm², using π = 22/7.
Relate it to the sphere

The curved surface area of a hemisphere is half the surface area of a complete sphere with the same radius.

Example: If a sphere has surface area 616 cm², the curved surface area of its hemisphere is 616/2 = 308 cm².
Check the required surface

Use 2πr² for only the curved part. Add πr² only when the flat circular base is also included.

Example: For r = 7 cm, curved area = 308 cm², while total surface area = 3 × 22/7 × 49 = 462 cm².

Curved Surface Area of Hemisphere Concepts

Using the Radius in the Formula

If the radius is known, calculate the curved surface area with CSA = 2πr².

Square the radius first, multiply by 2π, and write the result in square units. Use π = 22/7 when the radius is a suitable multiple of 7, or use π = 3.14 when specified.

Example: For r = 3.5 cm, CSA = 2 × 22/7 × 3.5² = 77 cm².

Using the Diameter

If the diameter d is given, use CSA = πd²/2.

The radius is half the diameter, so r = d/2. Therefore, 2π(d/2)² simplifies to πd²/2. This formula gives only the rounded surface area.

Example: For d = 10 cm, CSA = π × 10²/2 = 50π cm², approximately 157 cm² when π = 3.14.

Curved Surface Area versus Total Surface Area

Curved surface area excludes the circular base, whereas total surface area includes it.

For radius r, curved surface area is 2πr². The base has area πr², so total surface area is 2πr² + πr² = 3πr². Do not use the total surface area formula when the question asks for only the curved part.

Example: For r = 4 cm, CSA = 32π cm² and TSA = 48π cm².

Units and Square Conversion

Curved surface area is measured in square units, such as cm², m² or km².

Convert the radius or diameter to one unit before applying the formula. For area conversion, 1 m² = 10,000 cm² and 1 cm² = 100 mm².

Example: If r = 0.7 m, CSA = 2 × 22/7 × 0.7² = 3.08 m² = 30,800 cm².

Curved Surface Area of Hemisphere Visual Guide & Data

Use the table and chart below to understand the data better.

Hemisphere Surface Area Formula Comparison

The formulas differ according to whether the circular base is included.

Surface considered Formula Base included?
Curved surface only 2πr² No
Circular base only πr² Yes, base only
Total surface 3πr² Yes

Note: Here, r denotes the radius of the hemisphere.

Curved Surface of a Hemisphere

Visual guide: Curved Surface of a Hemisphere
Radius: r = 7 cm Curved surface area: 2πr² Circular base: excluded
The shaded rounded part represents the curved surface; the circular base is excluded from CSA.

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Practice Curved Surface Area of Hemisphere Questions

Practise published questions related to this topic.

1The price of petrol is increased by 28%. A person wants to increase his expenditure by 22% only. By approximately what percent should he decrease his consumption?→ 2An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article?→ 321.6 ÷ 3.6 × 2 + 0.25 × 16 ÷ 4 - 6 is equal to∶→ 4What is the value of x so that the seven digit number 55350x2 is divisible by 72?→ 5Two articles are sold for Rs. 4,752 each. On one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percentage, correct to one decimal place?→ 6The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?→ 7The value of 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is equal to:→ 8What is the value of x so that the seven digit number 8439x53 is divisible by 99?→ 9Two articles are sold for Rs. 962 each. On one, the seller gains 30% and on the other he loses 26%. What is his overall gain or loss percentage, nearest to one decimal place?→ 10An article is sold for Rs. 288 after successive discounts of 25% and x%. If the marked price of the article is Rs. 480, what is the value of x?→

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Quick Revision Notes

Curved Surface Area of Hemisphere: Revision Points

Use these formulas and rules for quick revision.

  • Curved surface area of a hemisphere = 2πr².
  • If diameter d is given, curved surface area = πd²/2.
  • The circular base is excluded from curved surface area.
  • Total surface area of a hemisphere = 3πr².
  • Use square units for area answers.
  • Convert all measurements to the same unit before calculation.
  • For r = 7 cm and π = 22/7, curved surface area = 308 cm².

Related Topic Explainers

Area of Square → Perimeter of Square → Area of Rectangle → Perimeter of Rectangle → Area of Triangle → Perimeter of Triangle → Heron's Formula → Area of Triangle Using Two Sides and Included Angle →

Curved Surface Area of Hemisphere FAQs

What is the curved surface area of a hemisphere with radius 14 cm?

CSA = 2πr² = 2 × 22/7 × 14² = 1,232 cm².

What is the curved surface area of a hemisphere with diameter 28 cm?

Use CSA = πd²/2. Thus, CSA = 22/7 × 28²/2 = 1,232 cm².

What is the difference between curved surface area and total surface area of a hemisphere?

Curved surface area excludes the circular base and equals 2πr². Total surface area includes the base and equals 3πr².

If the curved surface area of a hemisphere is 154 cm², what is its radius using π = 22/7?

2πr² = 154 gives r² = 24.5, so r = √24.5 cm, approximately 4.95 cm.

What happens to the curved surface area if the radius is doubled?

It becomes four times the original area because CSA is proportional to r². If the original area is A, the new area is 4A.

What is the curved surface area of a hemisphere with radius 3 cm using π = 3.14?

CSA = 2 × 3.14 × 3² = 56.52 cm².

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