Cylindrical container is to be constructed to be open at the top with a volume of 27π cubic meters using the least amount of material. find the radius and height of the cylinder which will require the least amount of material to construct.

radius comes out to be 3 m

height of the cylinder comes out to be 3m

Explanation:

given

volume of cylinder = 27π m³

π r² h = 27π

   r² h = 27.............(1)

surface area of cylinder open at the top

S = 2πrh + π r²

for least amount of material requirement.

hence radius comes out to be 3 m

for height put the value in the equation 1

so, height of the cylinder comes out to be 3m

it is given that trillions of microbes make up to 1% to 3% of the body mass.

let's take average of this percentage: 2%

consider the average mass of the human body as 70 kg.

then, trillions of microbes would have mass  

therefore, 100 trillion micro-organisms would weigh:

this is an approximate value and could change depending on the mass of the human body and percentage of the microbes present in it.

average mass per microorganism =