Question

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

Answer 1

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

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)

Answer 2

Ratio of surface area = 25/16

Ratio of volume = 125/64

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