If there is an error of $0.01 c m$ in the diameter of a sphere then percentage error in surface area when the radius $= 5 c m$ , is

0.005 %

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.05 %

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.1 %

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.2 %

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $0.2 %$
Surface area of sphere $S = 4 π r^{2}$
$S = π D^{2}$
$\Rightarrow S = 100 π$
Also, $\frac{d S}{d D} = 2 π D = 20 π$ [r=5]
Approximate error in S is
$d S = (\frac{d S}{d D}) Δ D$
$= 20 π (0.01)$
then
$\frac{d S}{S} = \frac{1}{500}$
$d S = 0.2$ % of S
Percentage error in $S = 0.2$

Suggest Corrections

Similar questions

Q. If there is an error of

\pm 0.04

cm in the measurement of the diameter of a sphere then the approximate percentage error in its volume, when the radius is

10 c m

, is

There is an error of $\pm$ 0.04cm in the measurement of the diameter of a sphere. When the radius is 10cm,the percentage error in the volume of the sphere is

Q. What is the percentage error in the surface area of a sphere, when the error in measuring its radius is

\pm

4%?

There is an error of $\pm$ 0.04cm in the measurement of the diameter of a sphere. When the radius is 10cm,the percentage error in the volume of the sphere is

Q. If the length of a cylinder is measured to be

4.28 cm

with an error of

0.01 cm

, then the percentage error in the measurement will be

Join BYJU'S Learning Program

If there is an error of 0.01cm in the diameter of a sphere then percentage error in surface area when the radius =5cm, is

The correct option is D 0.2%Surface area of sphere S=4πr2S=πD2⇒S=100πAlso, dSdD=2πD=20π [r=5]Approximate error in S is dS=(dSdD)ΔD=20π(0.01)thendSS=1500dS=0.2% of SPercentage error in S=0.2

If there is an error of $0.01 c m$ in the diameter of a sphere then percentage error in surface area when the radius $= 5 c m$ , is