math for homework

Question

The height of a right cylinder is r , where r is the radius. Write a function f in simplest form that represents the ratio of the volume to the surface area.

Answer 1

So looks like this problem is a bit easier since ‘r’ is the height and radius of your cylinder.

Surface area(S)= Curved Surface area + Area of The 2 bases of Cylinder

= [(2*Pi) * radius * Height] + [ 2 * pi * r * r ]

= [(2 * pi) * (r * r)] + [ 2 * pi * r * r] )

Now we’re gonna write S in a Neater way as follows :

S = [(2 * pi) * (r * r)] + [ 2 * pi * r * r] )

= 4 * Pi * r * r

Volume of cylinder( V) = Area of base of cylinder * height of cylinder = (pi * r * r) * r

To find Ratio( lets call it f ) of Volume to surface Area you have to :

DIVIDE Volume( V) by Surface area

So f = V / D

=. ( Pi * r * r * r ) / ( Pi * r * r * 4)

= r / 4

We get this answer since Pi * r * r is cancelled from both numerator and denominator.

So the function we found for the ratios is : Function (f )= r / 4

Answer 2

Typically the height of a right cylinder is labeled "h" so I assume you just made a typo in calling it "r".

V = πr²h

SA = 2πr² + 2πrh = πr(2r + 2h)

The ratio of V/SA = πr²h/[πr(2r + 2h)] = rh/(2r + 2h)

If you REALLY meant to say the the height is also "r", then we would replace the "h" in the ratio we got with "r" to get: r²/(2r + 2r) = r²/(4r) = r/4

Answer 3

Volume = πr²r= πr³

Surface Area = 2πrr = 2πr²

Volume : Surface Area π

πr^{3 /} 2πr² = r/2