The Curved surface area of hemisphere of diameter 1 is ______.

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2 π r 2

3 π r 2

4 π r 2

8 π r 2

answer is B.

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Detailed Solution

We know that a sphere is a locus of points in space that are equal distance from a fixed point. The fixed point is called the centre. The line segment that passes through the centre of the sphere is called the diameter of the sphere and the line segment joining the centre of the sphere to a point of the sphere is called the radius, commonly denoted as r.

https://www.vedantu.com/question-sets/0d9935a4-a93d-4a77-9f50-9bdb0ee6acee8800642171353755922.png

The amount of region covered by the outer surface of the sphere is called the curved surface area of the sphere and the curved surface area (CSA) of the sphere is given by

C S A = 4 π r 2

We know that a hemisphere is obtained when we cut a sphere into two equal halves with a plane containing the centre of the sphere. So the surface of the sphere will be cut into two equal halves. So the curved surface area of the hemisphere will be half of the surface area of the sphere that means with radius r as;

C S A = 12 4 π r 2 = 2 π r 2

We are asked in the question to find the curved surface area of a hemisphere with diameter 2r We know the radius is always half of the diameter. So the radius of the given hemisphere is