Answer :
Answer:
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)
Answer:
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