Little susie is enjoying a nice spherical lollipop. she sucks the lollipop in such away that the circumference decreases by 1 centimeter per minute. how fast is the volume of herlollipop changing when the lollipop has a radius of 5 centimeters? remember to include units

-50 cm^3/min

Explanation:

The volume of the lollipop is given by

where r is the radius in centimeters.

To find how fast the volume changes, we need to find the rate of change of the volume, which is given by its derivative with respect to time:

(1)

where

dr/dt is the rate of change of the radius

We know that the circumference is

and it decreases by 1 cm per minute, so

(cm/min)

from which we find dr/dt:

Substituting into (1),

 (cm^3/min)

And substituting r = 5, we find the rate of change of the volume when the radius is 5 cm:

(cm^3/min)

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

radiation

explanation:

heat is transmitted by radiation