Volume and Surface Area of Spheres

Volume and surface area of cube and cuboid

Real life questions about volume and surface area of prism grade 6

Cells of different organisms and even cells within the same organism are very diverse in terms of shape, size, and internal organization. One theme that occurs again and again throughout biology is that form follows function. In other words, a cell’s function influences its physical features. Cell Shape The diversity in cell shapes reflects the different functions of cells. Compare the cell shapes shown in Figure 4-4. The long extensions that reach out in various directions from the nerve cell shown in Figure 4-4a allow the cell to send and receive nerve impulses. The flat, platelike shape of skin cells in Figure 4-4b suits their function of covering and protecting the surface of the body. As shown below, a cell’s shape can be simple or complex depending on the function of the cell. Each cell has a shape that has evolved to allow the cell to perform its function effectively. SECTION 2 OBJECTIVES ● Explain the relationship between cell shape and cell function. ● Identify the factor that limits cell size. ● Describe the three basic parts of a cell. ● Compare prokaryotic cells and eukaryotic cells. ● Analyze the relationship among cells, tissues, organs, organ systems, and organisms. VOCABULARY plasma membrane cytoplasm cytosol nucleus prokaryote eukaryote organelle tissue organ organ system Cells have various shapes. (a) Nerve cells have long extensions. (b) Skin cells are flat and platelike. (c) Egg cells are spherical. (d) Some bacteria are rod shaped. (e) Some plant cells are rectangular. FIGURE 4-4 (a) Nerve cell (b) Skin cells (c) Egg cell (d) Bacterial cells (e) Plant cells Copyright © by Holt, Rinehart and Winston. All rights reserved. 1. All cubes have volume and surface area. The total surface area is equal to the sum of the areas of each of the six sides (area = length X width). 2. If you split the first cube into eight smaller cubes, you get 48 sides. The volume remains constant, but the total surface area doubles. 3. If you split each of the eight cubes into eight smaller cubes, you have 64 cubes that together contain the same volume as the first cube. The total surface area, however, has doubled again. CELL STRUCTURE AND FUNCTION 73 Cell Size Cells differ not only in their shape but also in their size. A few types of cells are large enough to be seen by the unaided human eye. For example, the nerve cells that extend from a giraffe’s spinal cord to its foot can be 2 m (about 6 1/2 ft) long. A human egg cell is about the size of the period at the end of this sentence. Most cells, how- ever, are only 10 to 50 μm in diameter, or about 1/500 the size of the period at the end of this sentence. The size of a cell is limited by the relationship of the cell’s outer surface area to its volume, or its surface area–to-volume ratio. As a cell grows, its volume increases much faster than its surface area does, as shown in Figure 4-5. This trend is important because the materials needed by a cell (such as nutrients and oxygen) and the wastes produced by a cell (such as carbon dioxide) must pass into and out of the cell through its surface. If a cell were to become very large, the volume would increase much more than the surface area. Therefore, the surface area would not allow materials to enter or leave the cell quickly enough to meet the cell’s needs. As a result, most cells are microscopic in size. Comparing Surface Cells Materials microscope, prepared slides of plant (dicot) stem and ani- mal (human) skin, pencil, paper Procedure Examine slides by using medium magnification (100). Observe and draw the sur- face cells of the plant stem and the animal skin. Analysis How do the surface cells of each organism differ from the cells beneath the surface cells? What is the function of the surface cells? Explain how surface cells are suited to their function based on their shape. Quick Lab Small cells can exchange substances more readily than large cells because small objects have a higher surface area–to-volume ratio. FIGURE 4-5 mb06se_csfs02.qxd 5/18/07 10:54 AM Page 73 74 CHAPTER 4 BASIC PARTS OF A CELL Despite the diversity among cells, three basic features are common to all cell types. All cells have an outer boundary, an interior sub- stance, and a control region. Plasma Membrane The cell’s outer boundary, called the plasma membrane (or the cell membrane), covers a cell’s surface and acts as a barrier between the inside and the outside of a cell. All materials enter or exit through the plasma membrane. The surface of a plasma mem- brane is shown in Figure 4-6a. Cytoplasm The region of the cell that is within the plasma membrane and that includes the fluid, the cytoskeleton, and all of the organelles except the nucleus is called the cytoplasm. The part of the cytoplasm that includes molecules and small particles, such as ribosomes, but not membrane-bound organelles is the cytosol. About 20 percent of the cytosol is made up of protein. Control Center Cells carry coded information in the form of DNA for regulating their functions and reproducing themselves. The DNA in some types of cells floats freely inside the cell. Other cells have a mem- brane-bound organelle that contains a cell’s DNA. This membrane- bound structure is called the nucleus. Most of the functions of a eukaryotic cell are controlled by the cell’s nucleus. The nucleus is often the most prominent structure within a eukaryotic cell. It maintains its shape with the help of a protein skeleton called the nuclear matrix. The nucleus of a typical animal cell is shown in

Surface area and Volume of prisms and pyramids

E+CZE The Surface Area and Volume of the 3d shapes.

ICSE Mathematics grade 9 CHP-20 Solids- Surface Area and volume of 3D solids

Cell Size Cells differ not only in their shape but also in their size. A few types of cells are large enough to be seen by the unaided human eye. For example, the nerve cells that extend from a giraffe’s spinal cord to its foot can be 2 m (about 6 1/2 ft) long. A human egg cell is about the size of the period at the end of this sentence. Most cells, how- ever, are only 10 to 50 μm in diameter, or about 1/500 the size of the period at the end of this sentence. The size of a cell is limited by the relationship of the cell’s outer surface area to its volume, or its surface area–to-volume ratio. As a cell grows, its volume increases much faster than its surface area does, as shown in Figure 4-5. This trend is important because the materials needed by a cell (such as nutrients and oxygen) and the wastes produced by a cell (such as carbon dioxide) must pass into and out of the cell through its surface. If a cell were to become very large, the volume would increase much more than the surface area. Therefore, the surface area would not allow materials to enter or leave the cell quickly enough to meet the cell’s needs. As a result, most cells are microscopic in size. Comparing Surface Cells Materials microscope, prepared slides of plant (dicot) stem and ani- mal (human) skin, pencil, paper Procedure Examine slides by using medium magnification (100). Observe and draw the sur- face cells of the plant stem and the animal skin. Analysis How do the surface cells of each organism differ from the cells beneath the surface cells? What is the function of the surface cells? Explain how surface cells are suited to their function based on their shape. Quick Lab Small cells can exchange substances more readily than large cells because small objects have a higher surface area–to-volume ratio. FIGURE 4-5 mb06se_csfs02.qxd 5/18/07 10:54 AM Page 73 74 CHAPTER 4 BASIC PARTS OF A CELL Despite the diversity among cells, three basic features are common to all cell types. All cells have an outer boundary, an interior sub- stance, and a control region. Plasma Membrane The cell’s outer boundary, called the plasma membrane (or the cell membrane), covers a cell’s surface and acts as a barrier between the inside and the outside of a cell. All materials enter or exit through the plasma membrane. The surface of a plasma mem- brane is shown in Figure 4-6a. Cytoplasm The region of the cell that is within the plasma membrane and that includes the fluid, the cytoskeleton, and all of the organelles except the nucleus is called the cytoplasm. The part of the cytoplasm that includes molecules and small particles, such as ribosomes, but not membrane-bound organelles is the cytosol. About 20 percent of the cytosol is made up of protein. Control Center Cells carry coded information in the form of DNA for regulating their functions and reproducing themselves. The DNA in some types of cells floats freely inside the cell. Other cells have a mem- brane-bound organelle that contains a cell’s DNA. This membrane- bound structure is called the nucleus. Most of the functions of a eukaryotic cell are controlled by the cell’s nucleus. The nucleus is often the most prominent structure within a eukaryotic cell. It maintains its shape with the help of a protein skeleton called the nuclear matrix. The nucleus of a typical animal cell is shown in Figure 4-6b. Most animal cells have a cell membrane, a nucleus, and a variety of other organelles embedded in a watery substance. The surface of the cell membrane can be seen in (a). The organelles inside the cell are labeled in the diagram (b). FIGURE 4-6 (a) (b) Mitochondrion Microfilaments Lysosome Golgi apparatus Smooth ER Ribosomes Cell membrane Microtubules Rough ER Nuclear pore Nuclear envelope Nucleolus Nucleus Copyright © by Holt, Rinehart and Winston. All rights reserved. Cell wall Ribosome Cell membrane Peptidoglycan Pili Flagellum DNA CELL STRUCTURE AND FUNCTION 75 A prokaryotic cell lacks a membrane- bound nucleus and membrane-bound organelles. Most prokaryotic cells are much smaller than eukaryotic cells are. FIGURE 4-7 A white blood cell (eukaryotic) changes shape as it attacks purple- stained bacterial cells that are much smaller (prokaryotic). FIGURE 4-8 TWO BASIC TYPES OF CELLS Fossil evidence suggests that the earliest cells on Earth were simple cells similar to some present-day bacteria. As cells evolved, they differentiated into two major types: prokaryotes and eukaryotes. Prokaryotes Prokaryotes (proh-KAR-ee-OHTS) are organisms that lack a membrane- bound nucleus and membrane-bound organelles. Although prokaryotic cells lack a nucleus, their genetic information—in the form of DNA—is often concentrated in a part of the cell called the nucleoid. Figure 4-7 shows a typical prokaryotic cell. Prokaryotes are divided into two domains: Bacteria and Archaea (ahr-KEE-uh). The domain Bacteria includes organisms that are similar to the first cellular life-forms. The domain Archaea includes organisms that are thought to be more closely related to eukaryotic cells found in all other kingdoms of life. Eukaryotes Organisms made up of one or more cells that have a nucleus and membrane-bound organelles are called eukaryotes (yoo-KAR-ee-OHTS). Eukaryotic cells also have a variety of subcellular structures called organelles, well-defined, intracellular bodies that perform specific functions for the cell. Many organelles are surrounded by a mem- brane. The organelles carry out cellular processes just as a person’s pancreas, heart, and other organs carry out a person’s life processes. Eukaryotic cells are generally much larger than prokary- otic cells, as seen in Figure 4-8, which shows a white blood cell (eukaryote) destroying tiny bacterial cells (prokaryotes).

SYI-1.D: Describe the structure and/ or function of subcellular components and organelles. ★ SYI-1.E: Explain how subcellular components and organelles contribute to the function of the cell. ★ SYI-1.F: Describe the structural features of a cell that allow organisms to capture, store, and use energy. ★ ENE-1.B: Explain the effect of surface area-to-volume ratios on the exchange of materials between cells or organisms and the environment. ★ ENE-1.C: Explain how specialized structures and strategies are used for the efficient exchange of molecules to the environment. ★ ENE-2.A: Describe the roles of each of the components of the cell membrane in maintaining the internal environment of the cell. ★ ENE-2.B: Describe the Fluid Mosaic Model of cell membranes. ★ ENE-2.C: Explain how the structure of biological membranes influences selective permeability. ★ ENE-2.D: Describe the role of the cell wall in maintaining cell structure and function. ★ ENE-2.E: Describe the mechanisms that organisms use to maintain solute and water balance. ★ ENE-2.F: Describe the mechanisms that organisms use to transport large molecules across the plasma membrane. ★ ENE-2.G: Explain how the structure of a molecule affects its ability to pass through the plasma membrane. ★ ENE-2.H: Explain how concentration gradients affect the ★ movement of molecules across membranes. ★ ENE-2.I: Explain how osmoregulatory mechanisms contribute to the health and survival of organisms. ★ ENE-2.J: Describe the processes that allow ions and other molecules to move across membranes. ★ ENE-2.K: Describe the membrane-bound structures of the eukaryotic cell. ★ ENE-2.L: Explain how internal membranes and membrane- bound organelles contribute to compartmentalization of eukaryotic cell functions. ★ EVO-1.A: Describe similarities and/or differences in compartmentalization between prokaryotic and eukaryotic cells. ★ EVO-1.B: Describe the relationship between the functions of endosymbiotic organelles and their free-living ancestral counterparts

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