Fruits form from a mature flower ovary. As seeds develop from the ovules contained within, the ovary wall undergoes a series of complex changes to form fruit. In some fruits, such as soybeans, the ovary wall dries; in other fruits, such as grapes, it remains fleshy. In some cases, organs other than the ovary contribute to fruit formation; such fruits are called accessory fruits.

The Theorem of Pappus, also known as the Pappus–Guldinus Theorem, provides a geometric method for determining the volume and surface area of solids generated by the revolution of a plane region or a plane curve about an external axis. The theorem consists of two related statements. The first addresses the volume of solids formed by rotating plane areas, while the second addresses the surface area generated by rotating plane curves. Both results depend on the location of the centroid, which...

The female breast is a hemispheric projection of variable size positioned anterior to the pectoralis major and serratus anterior muscles. A fascia layer composed of dense, irregular connective tissue connects it to these muscles.
Each breast features a pigmented projection known as the nipple, through which milk emerges via closely spaced openings of ducts, referred to as lactiferous ducts. Surrounding the nipple is a circular pigmented area of skin named the areola, which appears rough due to...

The pineal gland, a diminutive endocrine structure named for its pinecone-shaped appearance, is situated atop the third ventricle within the diencephalon region of the forebrain. This gland, composed of secretory cells known as pinealocytes arranged in compact cords and clusters around dense particles of calcium salts, plays a pivotal role in hormonal regulation.
The primary secretion of the pineal gland is the hormone melatonin, derived from serotonin. The concentration of melatonin in the...

Flowers are the reproductive, seed-producing structures of angiosperms. Typically, flowers consist of sepals, petals, stamens, and carpels. Sepals and petals are the vegetative flower organs. Stamens and carpels are the reproductive organs.

The two theorems developed by Pappus and Guldinus are widely used in mathematics, engineering, and physics to find the surface area and volume of any body of revolution. This is done by revolving a plane curve around an axis that does not intersect the curve to find its surface area or revolving a plane area around a non-intersecting axis to calculate its volume.
For finding the surface area, consider a differential line element that generates a ring with surface area dA when revolved.