What are the surface area and volume ratios of a cylinder change if the radius and height are multiplied by 5/4?

Ratio of surface area = 25/16

Ratio of volume = 125/64

Step-by-step explanation:

The surface area and volume of a cylinder are given by the formulas:

Surface area = 2 * (pi*r^2 + pi*r*h)

Volume = pi*r^2*h

If we increase the radius and height by 5/4, we have that:

New surface area = 2 * (pi * (5/4*r) ^2 + pi * (5/4) * r * (5/4) * h) = (5/4) ^2 * 2 * (pi*r^2 + pi*r*h) = (5/4) ^2 * Surface area

New volume = pi * (5/4*r) ^2 * (5/4) * h = (5/4) ^3 * pi*r^2*h = (5/4) ^3 * Volume

So the ratios are:

ratio of surface area = New surface area / Surface area = (5/4) ^2 = 25/16

ratio of volume = New volume / Volume = (5/4) ^3 = 125/64

The ratio of the surface areas and volume is 8 ((5y+5x) / 25xy)

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes.

Let us assume that the radius = x

Radius r=5x/4

And the height = y

Height h = 5y/4

We know that the total surface area of a cylinder is

A total = 2πrh+2πr²

We can factor out 2πr

A total = 2πr (h+r)

The volume of a cylinder is given as

v = πr²h

The surface area and volume ratios

Can be expressed as

2πr (h+r) / πr²h = 2 (h+r) / rh

= (2h+2r) / rh = 2h/rh + 2r/rh

= 2/r + 2/h

= 2 (1/r + 1/h)

Substituting our value of x and y

For radius and height we have

= 2 (1/5x/4 + 1/5y/4)

=2 (4/5x + 4/5y)

=2*4 (1/5x + 1/5y)

= 8 (5y+5x/25xy)