As the surface area of the cylindrical can is fixed, the radius and height of the can are in an inverse relationship: as one increases the other decreases.
Neither can go negative.
When the radius is 0, the volume is zero
When the height is 0, the volume is zero
Somewhere in between the volume reaches a maximum value.
To solve this, you need to specify the radius in terms of the height (or vice-versa), which can be done form the fixed surface area of the can.
The volume can then be specified in terms of only either the height or radius, which allows the maximum to be found (when the volume differentiated in terms of height or radius (that is dV/dh or dV/dr) is equal to zero).
You now have the How-to to solving the problem. Have a go before looking at applying the How-to requested (above) to the given surface area below.
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Surface area (A) = 2πr² + 2πrh
→ h = (A - 2πr²)/2πr
Volume (V) = πr²h
= πr²(A - 2πr²)/2πr
= r(A - 2πr²)/2
= Ar/2 - πr³
dV/dr = 0 when V is a maximum
dV/dr = d/dr (Ar/2 - πr³)
= A/2 - 3πr²
→ r = (A/(6π))^(1/2)
V = Ar/2 - πr³
→ Vmax = (A/2)( (A/(6π))^(1/2) ) - π(A/(6π))^(3/2)
= (6π/2)( (A/(6π))^(3/2) ) - π(A/(6π))^(3/2)
= 2π(A/(6π))^(3/2)
The value of A at 450 cm² can now be used to find the maximum volume:
Vmax = 2π(450cm²/(6π))^(3/2)
= 2π(75/π))^(3/2) cm³
≈ 1837 cm³
Flatworms have a higher surface area/volume ratio compared to a cylindrical worm, this is one of the reasons for flatworms to have the structure they do.
times leagth times weith
8pi m2 ~ 25.1327412 m2
To determine the area of a cylindrical box, you need to calculate the sum of the areas of its curved surface and its two circular bases. The formula for the curved surface area is given by 2πrh, where r is the radius of the base and h is the height of the box. The formula for the area of the circular base is πr^2. Add the two areas together to get the total surface area of the cylindrical box.
A cylinder has one closed "cylindrical" (circular) surface and two circles at each end. ======================
Flatworms have a higher surface area/volume ratio compared to a cylindrical worm, this is one of the reasons for flatworms to have the structure they do.
Biggest surface area to volume ratio.
Volcano!
times leagth times weith
not one circularity that is section of cylindrical surface with in any one of line with in as per tolerance on axis , and cylindrical not one that is entire surface required of with in tolerance according in the axis that is difference
Volcanic Vent.
The largest layer of the Earth's surface is the mantle.
A cylindrical protist has a higher surface are to volume ratio. This is because of the physical properties of spheres (some rather complicated math proves that spheres hold the most volume for their area).
8pi m2 ~ 25.1327412 m2
The speeds for grinding are not measured in RPMs. They are measured by peripheral wheel speed in surface feet per minute.Ê
To determine the area of a cylindrical box, you need to calculate the sum of the areas of its curved surface and its two circular bases. The formula for the curved surface area is given by 2πrh, where r is the radius of the base and h is the height of the box. The formula for the area of the circular base is πr^2. Add the two areas together to get the total surface area of the cylindrical box.
Water's surface tension and heat storage capacity is accounted by itsHydrogen Bonds