Physics Q81 – AP-EAMCET 2026

Home Physics Units & MeasurementsQuestion #545

Volume of a cylinder is given by

V = π r^{2} h

, here

r

is radius and

h

is height. The volume is measured with an error of

6 %

and height with an error of

4 %

, then error in radius is

Clue 1 of 3: Relationship between variables

Identify the formula that relates the volume, radius, and height of a cylinder.

🧠 Full Solution Path

Step 1: Express Radius in terms of Volume and Height✦ Active

The volume of a cylinder is given by the formula $V = π r^{2} h$ . We need to find the percentage error in the radius, given the percentage errors in volume and height. To do this, we first express the radius $r$ in terms of volume $V$ and height $h$ :

r^{2} = \frac{V}{π h}

r = {(\frac{V}{π h})}^{1 / 2}

💡 Teacher's Secret Hint

Remember that $π$ is a constant and does not contribute to the percentage error.

Step 2: Apply the Error Propagation Formula○ Expand

For a quantity $X = A^{a} B^{b}$ , the maximum fractional error is given by $\frac{Δ X}{X} = | a | \frac{Δ A}{A} + | b | \frac{Δ B}{B}$ . Applying this to our expression for $r$ :

\frac{Δ r}{r} = | \frac{1}{2} | \frac{Δ V}{V} + | - \frac{1}{2} | \frac{Δ h}{h}

\frac{Δ r}{r} = \frac{1}{2} \frac{Δ V}{V} + \frac{1}{2} \frac{Δ h}{h}

💡 Teacher's Secret Hint

Always use the absolute values of the powers when summing fractional errors to find the maximum possible error.

Step 3: Substitute Given Percentage Errors and Calculate○ Expand

We are given the percentage error in volume as $6 %$ and in height as $4 %$ . We can convert the fractional error formula to percentage error by multiplying by $100 %$ :

(\frac{Δ r}{r} \times 100 %) = \frac{1}{2} (\frac{Δ V}{V} \times 100 %) + \frac{1}{2} (\frac{Δ h}{h} \times 100 %)

Percentage error in r = \frac{1}{2} (6 %) + \frac{1}{2} (4 %)

Percentage error in r = 3 % + 2 %

Percentage error in r = 5 %

Thus, the error in the radius is $5 %$ .

💡 Teacher's Secret Hint

Ensure units are consistent throughout the calculation. Here, all values are already in percentages, simplifying the process.

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Physics Question 81 – AP-EAMCET 2026

Clue 1 of 3: Relationship between variables

🧠 Full Solution Path