This question can be addressed by simple calculus. As time (t) passes, the radius (r) of the circle increases at 4 feet per second. dr/dt = 4 The area of the circle is equal to pi multiplied by the square of the radius: A = pi x r2 From which we can infer that dA/dr = 2pi x r The radius, then, changes by four feet for every passing second. In turn, the area is increasing at a given moment by (2pi x r) square feet for every added radial foot. If we multiply square feet per footby feet per second we obtain square feet per second, as required by the question. This is the chain rule of differentiation.
dA/dt = dA/dr x dr/dt = 4 x 2pi x r = 8pi x r If r = 10 feet, then the area is momentarily increasing at 8pi x 10 = 80pi = 251 square feet per second.
The radius of a cylinder is half the thickness of its circular cross section.
if the speed is increasing at 3 m/s2 then that is the acceleration (if i understand the question correctly)
The circumference of a circle increases with an increase in the radius as it is directly proportional its radius.
The volume increases faster. (proportional to the cube of the radius)The surface area increases slower. (proportional to the square of the radius)
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The atomic radius decreases from left to right and increases from top to bottom
Increases
For circular motion, linear speed = angular speed (in radians) x radius. How the radius affects speed depends what assumptions you make about the problem. For example, if you assume the radius increases but the angular speed does not, then of course the linear speed will increase.
Given a constant velocity v, a radius r, the equation for the period T is given as:T = 2πr/vSo, as radius r increases, so does the period T.
atomic radius increases down a group as the number of shells increases
Going down and to the left on the periodic table, atomic radius increases. Therefore, the smallest atomic radius is that of Helium (He), and the largest is that of Francium (Fr). Coincidentally, these are also the most and least reactive elements.
Atomic radii increases moving down a group in the Periodic Table due to the increasing energy levels in the electron configuration and electrons filling in energy levels further away from the nucleus.
The periodic table is arranged in order (across and down the rows) in increasing number of protons in the nucleus; as the number of proton increases the radius of the nucleus generally increases - thus the order is the order reading down group 2: beryllium (least), magnesium, calcium, strontium, barium and radium (largest).
The atomic radius of elements increases as you go down a group. This increase in radius as you go down a period is primarily caused by the increasing principal quantum number of the outer electron shells.
The radius of a cylinder is half the thickness of its circular cross section.
if the speed is increasing at 3 m/s2 then that is the acceleration (if i understand the question correctly)
The circumference of a circle increases with an increase in the radius as it is directly proportional its radius.