
The curved surface area of a hemisphere with radius ‘r’ is ________
Answer
529.8k+ views
Hint: First of all, try to recollect all the areas related to the hemisphere. Now we know that the hemisphere is half of the sphere and the curved surface area of the hemisphere is only the area of its curved part or outer surface. So, we get the surface area of the sphere and its half would be the curved surface area of the hemisphere.
Complete step-by-step answer:
In this question, we have to find the curved surface area of a hemisphere of radius “r”. Let us first see the different areas for the hemisphere. We know that a hemisphere is formed when the plane cuts the sphere into two equal halves or we can also say that a sphere is a combination of the two hemispheres. The hemisphere of radius “r” is as shown below.
Now let us see the different areas of the hemisphere.
Total Surface Area: The area of the curved surface and the area of the circle (base) is called the total surface area.
Curved Surface Area: The area of the outer surface of the hemisphere is called the curved surface area.
From the surface area of a sphere, we can easily calculate the surface area of the hemisphere. Since the hemisphere is half of the sphere. So we get,
CSA of the hemisphere = surface area of the sphere
So we get the curved surface area of a hemisphere as square units.
Note: In this question, many students make this mistake of taking the half of the total surface area of the sphere which is and considering it as the total surface area of the hemisphere which is wrong. They must note that when we cut a sphere in two hemispheres, then apart from the curved part of the hemisphere, we get one more part and that is the circular base whose area is . So we get the total surface area of a hemisphere as whereas curved surface area of a hemisphere as .
Complete step-by-step answer:
In this question, we have to find the curved surface area of a hemisphere of radius “r”. Let us first see the different areas for the hemisphere. We know that a hemisphere is formed when the plane cuts the sphere into two equal halves or we can also say that a sphere is a combination of the two hemispheres. The hemisphere of radius “r” is as shown below.

Now let us see the different areas of the hemisphere.
Total Surface Area: The area of the curved surface and the area of the circle (base) is called the total surface area.
Curved Surface Area: The area of the outer surface of the hemisphere is called the curved surface area.
From the surface area of a sphere, we can easily calculate the surface area of the hemisphere. Since the hemisphere is half of the sphere. So we get,
CSA of the hemisphere =
So we get the curved surface area of a hemisphere as
Note: In this question, many students make this mistake of taking the half of the total surface area of the sphere which is
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 10 General Knowledge: Engaging Questions & Answers for Success

Master Class 10 Computer Science: Engaging Questions & Answers for Success

Master Class 10 Science: Engaging Questions & Answers for Success

Master Class 10 Social Science: Engaging Questions & Answers for Success

Master Class 10 Maths: Engaging Questions & Answers for Success

Master Class 10 English: Engaging Questions & Answers for Success

Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Which one is a true fish A Jellyfish B Starfish C Dogfish class 10 biology CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

What is the median of the first 10 natural numbers class 10 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE
