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If a radius of a sphere increase by a factor of 4 what does the factor of the volume increase?
64The formula to find the volume of a sphere is4/3 * pi * r3where r is the radius of the sphere. So if the radius is increased by a factor of 4, then the formula becomes4/3 * pi * (4r)3 = 4/3 * pi * 64r3showing that the volume increases by a factor of 64.
What is shape factor for sphere?
The shape factor for a sphere is a dimensionless quantity that characterizes its geometry in relation to its volume and surface area. It is defined as the ratio of the surface area of the sphere to the square of its radius, which is given by the formula ( \text{Shape Factor} = \frac{4\pi r^2}{(2r)^2} = \frac{4\pi r^2}{4r^2} = \pi ). This indicates that the shape factor for a sphere is constant and equal to ( \pi ), reflecting its uniformity in all directions.
When a spherical cell increases in diameter from 2 micrometers to 20 micrometers by what factor does its volume change?
The formula for volume of a sphere is (4/3)(pi)r3, where r is the radius. The initial volume of the sphere is then (4/3)(pi)(1)3 and the final volume is (4/3)(pi)(10)3. (Remember that we are given diameters, and need to divide them by two to find the radii to plug into the equations.)The factor by which the volume changes is (Final Volume)/(Initial Volume), which is this case is[ (4/3)(pi)(10)3 ] / [ (4/3)(pi)(1)3 ](4/3)pi cancels out, leaving 103 / 13 = 1000.
What is the reciprocal of 4 - pi?
pi-4 is the opposite and 1/4-pi is the reciprocal
What is the factor of Pi?
22 over 7
What is the exact value using a sum or difference formula of the expression cos 11pi over 12?
11pi/12 = pi - pi/12 cos(11pi/12) = cos(pi - pi/12) cos(a-b) = cos(a)cos(b)+sin(a)sin(b) cos(pi -pi/12) = cos(pi)cos(pi/12) + sin(pi)sin(pi/12) sin(pi)=0 cos(pi)=-1 Therefore, cos(pi -pi/12) = -cos(pi/12) pi/12=pi/3 -pi/4 cos(pi/12) = cos(pi/3 - pi/4) = cos(pi/3)cos(pi/4)+sin(pi/3) sin(pi/4) cos(pi/3)=1/2 sin(pi/3)=sqrt(3)/2 cos(pi/4)= sqrt(2)/2 sin(pi/4) = sqrt(2)/2 cos(pi/3)cos(pi/4)+sin(pi/3) sin(pi/4) = (1/2)(sqrt(2)/2 ) + (sqrt(3)/2)( sqrt(2)/2) = sqrt(2)/4 + sqrt(6) /4 = [sqrt(2)+sqrt(6)] /4 Therefore, cos(pi/12) = (sqrt(2)+sqrt(6))/4 -cos(pi/12) = -(sqrt(2)+sqrt(6))/4 cos(11pi/12) = -(sqrt(2)+sqrt(6))/4
How do you find the height of a cylinder if the surface area is 312 inches and the radius is 2 inches?
Entire surface area = (2*pi*4)+(4*pi*height) = 312 (4*pi*height) = 312-(2*pi*4) (4*pi*height) = 286.8672588 Divide both sides by 4*pi to find the height:- height = 22,82817112 inches Check: (2*pi*4)+(4*pi*22.82817112) = 312 square inches Formula: (2*pi*radius2)+(diameter*pi*height) = area
What is the exact value of the expression cos 7pi over 12 cos pi over 6 -sin 7pi over 12 sin pi over 6?
cos(a)cos(b)-sin(a)sin(b)=cos(a+b) a=7pi/12 and b=pi/6 a+b = 7pi/12 + pi/6 = 7pi/12 + 2pi/12 = 9pi/12 We want to find cos(9pi/12) cos(9pi/12) = cos(3pi/4) cos(3pi/4)= cos(pi-pi/4) cos(pi)cos(pi/4)-sin(pi)sin(pi/4) cos(pi)=-1 sin(pi)=0 cos(pi/4) = √2/2 sin(pi/4) =√2/2 cos(pi)cos(pi/4)-sin(pi)sin(pi/4) = - cos(pi/4) = -√2/2
What is the piston area of a cylinder bore of 2 inches?
Area = (Pi/4)*(dia2) = (Pi/4)*22 = (Pi/4)*4 = Pi sq.in = 3.1416 square inches.
What is 3pi covert to degree?
To convert (3\pi) radians to degrees, you can use the conversion factor (180^\circ/\pi). Multiply (3\pi) by this factor: [ 3\pi \times \frac{180^\circ}{\pi} = 3 \times 180^\circ = 540^\circ. ] Therefore, (3\pi) radians is equivalent to (540^\circ).
What are the distinct fourth root of -1?
The four roots are cos(theta)+i*sin(theta) where theta = pi/4, 3*pi/4, 5*pi/4 and 7*pi/4.
What is the formula of pi?
4-(4/3)+(4/5)-(4/7)+(4/9)-(4/11)....=pi There are no non-infinite serieses known for finding pi
