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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.
Which cell has the greater surface area compared to its volume the large cell or one of the smaller cells?
A smaller cell has a higher surface area to volume ratio. A reason for this is volume is cubic (3D) and surface area is 2D so when surface area increases a little bit, the volume increases exponentially. And when the surface area shrinks a little bit, the volume decreases exponentially.
Would a spherical protist or a cylindrical protist have a higher surface area to volume ratio?
A spherical protist would have a higher surface area to volume ratio compared to a cylindrical protist of the same size. This is because a sphere has the smallest surface area for a given volume, making it more efficient in terms of nutrient exchange and waste removal.
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.
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.
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.
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.
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.
What is the relationship between rate of ion exchange and surface to volume ratio?
The rate of ion exchange is typically faster with a higher surface to volume ratio. This is because a higher surface area allows for more contact points for ions to interact with the exchange material, increasing the efficiency of the process. A higher surface to volume ratio provides more active sites for ion exchange to occur, leading to a more rapid exchange rate.
