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Please I want to Know that if the radius of the black hole = 0 then how it have its surface and how it absorbs things?

$$\begin{align} g &= \frac{Gm}{0^2} \\ &= \infty \end{align}$$

then without surface and volume how it absorbs things?

Qmechanic
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Varun
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    Division by zero is undefined. It's only infinity in the limit and that depends on which side you approach zero from (though in this case it's squared so it doesn't matter). – Brandon Enright Aug 02 '14 at 07:01
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    There might be a good question hidden somewhere in this post, but it is not a good idea to start by extrapolating a formula $g=GM/r^2$ from Newtonian gravity to black hole physics. – Qmechanic Aug 02 '14 at 15:27

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Well, first off, the assumption that black holes have 0 radius is wrong. It is super dense. The singularity (the center of the black hole) has infinite density.

Source: http://en.wikipedia.org/wiki/Black_hole

Brandon Enright
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ParadoxicalUser
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    Your right the assumption is wrong but this doesn't exactly make for a complete answer either. Consider updating it to include more information. – Brandon Enright Aug 02 '14 at 07:00
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The first point is easy - your formula is wrong. The radius of a black hole is known as the Schwarzchild Radius, and is equal to 

                        R = 2Gm / c^2

While this is very small, it is not zero. As a result, the event horizon has a non-zero area. See http://en.wikipedia.org/wiki/Black_hole for more information.

WhatRoughBeast
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A black hole has two main features:

  1. a singularity
  2. an event horizon

The event horizon is a sphere with a certain radius. Most people visualize the singularity as a point at the center of the sphere, and although that's not quite rigorously right, it's good enough for the purposes of the present discussion.

Using a rough Newtonian analogy, the event horizon is like the surface from which the escape velocity exceeds the speed of light. In the real relativistic theory, it's boundary that no cause-and-effect relationships can cross from the inside out.

Black holes form by the gravitational collapse of massive bodies. You can think of the singularity as the place where all the in-falling matter accumulated.

When people talk about the radius of a black hole, they usually mean the radius of the event horizon.

without surface and volume how it absorbs things?

This depends on what you mean by "absorb." You could think of in-falling matter as being absorbed when it crosses the event horizon. The event horizon does have area and does contain an interior volume. If "absorption" means hitting the singularity, then the matter is infinitely compressed.