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Surface areas and volumes of spheres?
The formula for the surface area of a sphere is 4πr2. The formula for the volume of a sphere is 4/3πr3.
As the radius of a sphere gets larger which of the spheres measurements increases more the surface area or the volume?
The volume increases faster. (proportional to the cube of the radius)The surface area increases slower. (proportional to the square of the radius)
How does calculus impact your society?
The biggest impact I think of: Calculus is how people invented the formulas to get the volume and surface area of spheres/cones/pyramids.
Does a flat worm or a cylindrical worm have a higher surface area to volume ratio?
Flatworms have a higher surface area/volume ratio compared to a cylindrical worm, this is one of the reasons for flatworms to have the structure they do.
How do you find volume and surface area of composite figues?
To find the volume and surface area of composite figures, first break the figure down into simpler shapes (like prisms, cylinders, or spheres). Calculate the volume and surface area of each individual shape using their respective formulas. For volume, sum the volumes of the separate shapes, and for surface area, add the surface areas while ensuring to account for any overlapping areas that are not exposed. Finally, apply the appropriate units for both volume and surface area.
Would a spherical protist or a cylindrical protist have a higher surface area to volume ratio?
A cylindrical protist has a higher surface are to volume ratio. This is because of the physical properties of spheres (some rather complicated math proves that spheres hold the most volume for their area).
Which of the spheres measurements increases more the surface area or the volume?
If you increase the radius, the volume will increase more than the area.
Surface areas and volumes of spheres?
The formula for the surface area of a sphere is 4πr2. The formula for the volume of a sphere is 4/3πr3.
As the radius of a sphere gets larger which of the spheres measurements increases more the surface area or the volume?
The volume increases faster. (proportional to the cube of the radius)The surface area increases slower. (proportional to the square of the radius)
Which has the greater surface to volume ratio a tennis ball or a basketball explain. What could be done to increase the surface to volume ratio of both?
They are spheres. They cannot therefore have different geometrical properties. To alter surface to volume ratios you would need to alter the shape. The study of mathematical shapes is called topology.
Why are spheres important?
Spheres are important because they are geometric shapes that have the same radius from their center to all points on their surface, making them useful in various fields such as geometry, physics, and engineering. They have unique properties that allow for efficient packing of space, uniform distribution of stresses, and minimal surface area for a given volume, making them ideal for applications such as planetary bodies, bubbles, and particles in suspension.
What is the relationship between the percent volume not reached by the stain and the surface area-to-volume ratio?
The relationship between the percent volume (not reached by the stain) and the surface area-to-volume ratio would be that the bigger the agar cube size (surface area to volume ratio), the bigger the percent volume. This is true because resources need to travel a farther distance through the cell ("cover more ground", so to speak) in order to be evenly distributed through the cell.
How does calculus impact your society?
The biggest impact I think of: Calculus is how people invented the formulas to get the volume and surface area of spheres/cones/pyramids.
Does a flat worm or a cylindrical worm have a higher surface area to volume ratio?
Flatworms have a higher surface area/volume ratio compared to a cylindrical worm, this is one of the reasons for flatworms to have the structure they do.
How do you find volume and surface area of composite figues?
To find the volume and surface area of composite figures, first break the figure down into simpler shapes (like prisms, cylinders, or spheres). Calculate the volume and surface area of each individual shape using their respective formulas. For volume, sum the volumes of the separate shapes, and for surface area, add the surface areas while ensuring to account for any overlapping areas that are not exposed. Finally, apply the appropriate units for both volume and surface area.
What will happen to a spheres volume if the radius is tripled?
The volume increases 27-fold.
What happens to a cell's ratio of surface area to volume as the volume increases more rapidly than its surface area?
As volume increases surface area increase, but the higher the volume the less surface area in the ratio. For example. A cube 1mmx1mmx1mm has volume of 1mm3 surface area of 6mm2 which is a ration of 1:6 and a cube of 2mmx2mmx2mm has a volume of 8mm3 and surface area of 24mm2 which is a ratio of 1:3.
