Answer:
The new volume is 81.2% of the prior, this is true for any for any values of radius and height, as long as they are changed as stated.
Step-by-step explanation:
The volume of a cylinder is given by:
[tex]V = \pi*r^2*h[/tex]
If we increase the diameter by 15%, then the radius is increased by 7.5% and the new radius is:
[tex]r_{new} = 1.075*r[/tex]
If we decrease the height by 30%, then the new height is 70% of the prior and is given by:
[tex]h_{new} = 0.7*h[/tex]
Applying to the volume formula we have:
[tex]V_{new} = pi*(r_{new})^2*h_{new}[/tex]
[tex]V_{new} = \pi*(1.075*r)^2*0.7*h\\V_{new} = 1.16*0.7*\pi*r^2*h\\V_{new} = 0.812*\pi*r^2*h\\V_{new} = 0.812*V[/tex]
The new volume is 81.2% of the prior, this is true for any for any values of radius and height, as long as they are changed as stated.
