# Significant Figures: Cylinder Volume Calculation

• zorro
In summary, the volume of a cylinder with a length of 1.2 x 10^-2 m and a radius of 2.12 x 10^-2 m is 1.7 x 10^-5 m3, calculated using the formula V=(pi)r^2 l and rounding the intermediate result to the appropriate number of significant figures. The use of 22/7 for pi and rounding down intermediate results is not recommended.
zorro

## Homework Statement

The length of a cylinder is 1.2 x 10^-2 m and its radius is 2.12 x 10^-2 m. What is its volume according to significicant figures?

## The Attempt at a Solution

V=(pi)r^2 l
r^2 = 4.49 x 10^-4 (as radius has 3 significant digits)
V= 22/7 x 4.49 x 10^-4 x 1.2 x 10^-2
V= 22/7 x 5.4 x 10^-6 [4.49 x 10^-4 x 1.2 x 10^-2 = 5.388 x 10^-6 = 5.4 x 10^-6 as least no. of significant digits is 2 here)
so V=1.7 x 10^-5

1.7x10-5 m3 looks correct to me. But you should not use 22/7 for pi nor round down intermediate results.

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Intermediate results have to be rounded off in order to satisfy the rules of significant figures.

No. You should round them down only if you are displaying them, but you do the calculations using full accuracy.

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you mean to say that
5.388 x 10^-6 = 5.4 x 10^-6
should be written as 5.3 x 10^-6 ?

No, when displaying it should be written as 5.4x10-5, but for calculations you should use 5.388x10-5.

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## What are significant figures and why are they important in calculating cylinder volume?

Significant figures refer to the digits in a number that are reliable and accurate. They are important in calculating cylinder volume because they indicate the precision of the measurement and help to avoid errors in calculations.

## How do you determine the number of significant figures in a measurement?

The number of significant figures in a measurement is determined by counting all the digits that are known with certainty, plus one estimated digit. Leading zeros are not significant, while zeros between non-zero digits and trailing zeros after a decimal point are significant.

## What is the rule for rounding off calculated values using significant figures?

When rounding off calculated values using significant figures, the final answer should have the same number of significant figures as the original value with the least number of significant figures.

## Why is it necessary to use scientific notation when dealing with large or small numbers in cylinder volume calculations?

Scientific notation is necessary when dealing with large or small numbers in cylinder volume calculations because it makes it easier to write and understand very large or very small numbers. It also helps to maintain the correct number of significant figures in the final answer.

## Can significant figures be used when doing addition or subtraction of cylinder volumes?

Yes, significant figures can be used when doing addition or subtraction of cylinder volumes. The final answer should have the same number of decimal places as the original value with the least number of decimal places.

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