[Shishank Kumar]

1729, the is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 – cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729. It is known as the Hardy-Ramanujan Number.

[Shishank Kumar]

The volume of a right cylinder can be calculated using the formula:

V = πr^2h

where V is the volume, r is the radius of the base, and h is the height.

The diameter of the cylinder is 12 meters, so the radius is half of that, or 6 meters. The height of the cylinder is 16 meters.

Putting these values into the formula, we get:

V = π(6 meters)^2(16 meters)

V = 1,814.37 cubic meters (rounded to two decimal places)

Therefore, the volume of the tank is 1,814.37 cubic meters

[Shishank Kumar]

Physical change is a change of matter in which only physical properties such as color, physical taste, volume, density etc. change whereas the chemical composition of the matter remains unchanged.In other words, the substance undergoes a change in its appearance, state, or form, but its fundamental identity remains the same. Here are some examples of physical changes:

Changes in state: Melting of ice into water or freezing of water into ice.

Changes in shape or size: Cutting a piece of paper into smaller pieces or molding clay into different shapes.

Changes in texture: Crushing a rock into smaller particles or tearing a piece of cloth.

Changes in appearance: Dissolving salt in water or mixing different colors of paint.

A chemical change, also known as a chemical reaction, involves the transformation of substances into new substances with different chemical compositions and properties. During a chemical change, chemical bonds are broken and new bonds are formed, resulting in the creation of entirely new substances. Here are some examples of chemical changes:

Combustion: Burning of wood or paper, where they are converted into ash, smoke, and gases.

Oxidation: Rusting of iron, where iron reacts with oxygen in the presence of moisture to form iron oxide (rust).

Digestion: Conversion of food into simpler molecules through various chemical reactions in the digestive system.

Fermentation: Conversion of sugar into alcohol and carbon dioxide by yeast during the process of making bread or brewing beer.

Also, physical changes are alterations that affect the physical properties of a substance, such as its state, shape, or appearance, while chemical changes involve the formation of new substances with different chemical compositions through the breaking and forming of chemical bonds. Physical change is a temporary change and it is reversible in nature whereas chemical change is a permanent change and it is irreversible in nature.