To minimize neutron leakage from a reactor, the ratio of the surface area to the volume should be a minimum. For a given volume V the ratio of the sphere will be
.
We know that the surface area and volume of the sphere is given by:

Therefore, the ratio between the surface area and the volume for the sphere will be:

Equating the volume to the constant c, we will find the value of
.

Substituting the value of r in the ration between surface area and volume, we get:

Calculating the constants, we get:

Hence, the ration between surface area and volume is 
To learn more about surface area and volume of sphere, refer to:
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Answer:
Initial pressure = 6 atm. Work = 0.144 J
Explanation:
You need to know the equation P1*V1=P2*V2, where P1 is the initial pressure, V1 is the initial volume, and P2 and V2 are the final pressure and volume respectively. So you can rearrange the terms and find that (1.2*0.05)/(0.01) = initial pressure = 6 atm. The work done by the system can be obtained calculating the are under the curve, so it is 0.144J
Answer:
Explanation:
Given
Distance between two loud speakers 
Distance of person from one speaker 
Distance of person from second speaker 
Path difference between the waves is given by

for destructive interference m=0 I.e.




frequency is given by

where 

For next frequency which will cause destructive interference is
i.e.
and 


frequency corresponding to this is

for 


Frequency corresponding to this wavelength

<em>There are some placeholders in the expression, but they can be safely assumed</em>
Answer:
(a) 
(b) 
(c) 
(d) 
Explanation:
<u>Sinusoidal Waves
</u>
An oscillating wave can be expressed as a sinusoidal function as follows

Where



The voltage of the question is the sinusoid expression

(a) By comparing with the general formula we have


(b) The period is the reciprocal of the frequency:


Converting to milliseconds

(c) The amplitude is

(d) Phase angle:

maximum allowed value of the speed in roller coaster is given as

now from kinematics we can say

here initial speed will be

acceleration is due to gravity

now we can use this to find the height



so maximum allowed height will be 20.4 m