• The roots of a plant take up air from the spaces between the soil particles.
• Root hairs are in contact with the air in the soil particles. 
• Oxygen from the air in soil particles diffuse into root hair and reach all the cells of the root where it is utilised in respiration. Hence, roots respire through air spaces.

While plants can absorb water from many sources the best place for this is the root system which is in contact with the soil where most of the water is found. The root system is usually extensive and has root hairs which help increase the surface area for water absorption. Water enters the root hair cells and then moves from cell to cell till it reaches the root cortex it goes on to the xylem vessels to be transported to the leaves.

So, the correct option is 'Root hair'.

Aerobic respiration takes place in the mitochondria and requires oxygen and glucose, and produces carbon dioxide, water, and energy. The chemical equation is 

The process by which cells obtain chemical energy by the consumption of oxygen and the release of carbon dioxide is known as respiration. In order to carry on respiration, plant cells need oxygen and a means of disposing of carbon dioxide just as animal cells do. In plants, each part such as root, stem performs respiration because plants do not possess any specialized organs like animals for the exchange of gases. 

In plants respiration also takes place through roots. In soil oxygenated air is present in air spaces between soil particles. This oxygen is absorbed into the roots by root hair present on the roots. The hairs of the roots are in direct contact with them. In fact, a root hair is a lateral tubular outgrowth of the outer epidermal cells of a root. The oxygen present in between the soil particles diffuse into the root hairs. From root hairs, oxygen is supplied to all the parts of roots for respiration. During respiration, oxygen is converted into carbon dioxide gas which is diffused in opposite direction i.e. out of the roots by the same root hairs which complete the process of respiration in roots.

The process by which cells obtain chemical energy by the consumption of oxygen and the release of carbon dioxide is known as respiration. In order to carry on respiration, plant cells need oxygen and a means of disposing of carbon dioxide just as animal cells do. In plants, each part such as root, stem performs respiration because plants do not possess any specialized organs like animals for the exchange of gases.

The process of respiration is expressed as:

Glucose + Oxygen → Carbon Dioxide + Water (+ Energy)

Cellular respiration is the process by which cells in plants and animals break down sugar and turn it into energy, which is then used to perform work at the cellular level. The purpose of cellular respiration is simple, it provides cells with the energy they need to function. If living things could not get the energy they need out of food, it would be absolutely worthless. All living things would eventually die, no matter the quality and amount of food. Cellular respiration is used to create usable energy from the foods that living things eat. It's important to know that the reactions involved in cellular respiration are catabolic, meaning they break down molecules into smaller ones. This differs from anabolic reactions, which build bigger molecules from smaller ones. 

During respiration, due to consumption of organic resources in the cell the dry weight decreases. In respiration, there is a loss in dry weight.

Plant's roots are embedded into the soil. The soil has air spaces which allow the tip of the roots to take up oxygen and then this is transported to the other parts of the plant.