The dimensions of a cone are measured using a scale with a least count of 2 mm. The diameter of the base and the height are both measured to be 20.0 cm. The maximum percentage error in the determination of the volume is ____. [2024]

Question

The dimensions of a cone are measured using a scale with a least count of 2 mm. The diameter of the base and the height are both measured to be 20.0 cm. The maximum percentage error in the determination of the volume is ____. [2024]

Smart Achievers · Accepted Answer

(3)

$Volume of a cone = V = \frac{1}{3} π R^{2} H$

$\Rightarrow \frac{d V}{V} = 2 \cdot \frac{d R}{R} + \frac{d H}{H}$

$∴$ $Percentage error = [2 \times \frac{0.2}{20} + \frac{0.2}{20}] \times 100$

$= 3$

Solution

Q.
The dimensions of a cone are measured using a scale with a least count of 2 mm. The diameter of the base and the height are both measured to be 20.0 cm. The maximum percentage error in the determination of the volume is ____. [2024]

Ans.
(3)

$Volume of a cone = V = \frac{1}{3} π R^{2} H$

$\Rightarrow \frac{d V}{V} = 2 \cdot \frac{d R}{R} + \frac{d H}{H}$

$∴$ $Percentage error = [2 \times \frac{0.2}{20} + \frac{0.2}{20}] \times 100$

$= 3$

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Solution

Q. The dimensions of a cone are measured using a scale with a least count of 2 mm. The diameter of the base and the height are both measured to be 20.0 cm. The maximum percentage error in the determination of the volume is ____. [2024]

Ans. (3) Volume of a cone =V=13πR2H ⇒dVV=2·dRR+dHH ∴ Percentage error=[2×0.220+0.220]×100 =3

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Q.
The dimensions of a cone are measured using a scale with a least count of 2 mm. The diameter of the base and the height are both measured to be 20.0 cm. The maximum percentage error in the determination of the volume is ____. [2024]

Ans.
(3)

$Volume of a cone = V = \frac{1}{3} π R^{2} H$

$\Rightarrow \frac{d V}{V} = 2 \cdot \frac{d R}{R} + \frac{d H}{H}$

$∴$ $Percentage error = [2 \times \frac{0.2}{20} + \frac{0.2}{20}] \times 100$

$= 3$