Mathematics: A cylinder has a base diameter of 5 cm and a height of 8 cm. The base diameter is increased by 15% and the height is decreased by 30%. Find the percentage change in the volume of the cylinder. Type each step of your working on a separate line.

12 * 3x Step-by-step explanation:x is equal to the minutes...

A cylinder has a base diameter of 5 cm and a height

Qwerty2771

29.01.2022

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:

$V = \pi*r^2*h$

If we increase the diameter by 15%, then the radius is increased by 7.5% and the new radius is:

$r_{new} = 1.075*r$

If we decrease the height by 30%, then the new height is 70% of the prior and is given by:

$h_{new} = 0.7*h$

Applying to the volume formula we have:

$V_{new} = pi*(r_{new})^2*h_{new}$

$V_{new} = \pi*(1.075*r)^2*0.7*h\\V_{new} = 1.16*0.7*\pi*r^2*h\\V_{new} = 0.812*\pi*r^2*h\\V_{new} = 0.812*V$

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.

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