Question

if a solid right circular cylinder made of iron is heated to increase its radius and height by 1% each then by how much percent does the volume of the solid increase

Answer 1

Answer: The answer is 3.0301%.

Step-by-step explanation:  Given that a right circular cylinder is made of iron. This is heated to increase its radius and height each by 1%. We are to calculate the percentage by which the volume of the cylinder will increase.

We know that, if 'r' and 'h' be the radius and height of a right circular cylinder, then its volume will be

$V=\pi r^2h.$

Now, if radius and height are increased by 1%, then the new radius and height will be

$r'=r+1\%\times r=r+0.01r=1.01r,\\\\h'=h+1\%\times h=1.01h.$

Therefore, new volume will be

$V'=\pi r'^2h'=\pi(1.01r)^2(1.01h)=1.030301\pi r^2h.$

So, increase in the volume is

$I=V'-V=1.030301V-V=0.030301V.$

Thus, percentage of increase in volume will be

I% = 0.030301 × 100%=3.0301%.

Answer 2

Answer:

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