Question

The radius of a ball is (5.0+0.2) cm. The percentage error in the volume of the ball is :
(A). 12%
(B) 4%
(C) 7%
(D) 9%​

Answer 1

Answer ⇒ Option (A). is correct.

Explanation ⇒

Given, Radius of the ball = 5 cm. ± 0.2 cm.

∴ % error = % error in radius/total radius × 100

∴ % error = 0.2/5 × 100 = 4 %

Now, ball is spherical in shape, thus, Volume = 4/3 × πr³

This means, volume is proportional to the third power of radius.

∴ % Error of Volume = 3 × % Error of Radius.

∴ % error of volume = 3 × 4 %

∴ Error in volume = 12 %.

Hence, the %error of volume = 12 %.

Hope it helps.

Answer 2

Answer ⇒ Option (A). is correct.

Explanation ⇒

Given, Radius of the ball = 5 cm. ± 0.2 cm.

∴ % error = % error in radius/total radius × 100

∴ % error = 0.2/5 × 100 = 4 %

Now, ball is spherical in shape, thus, Volume = 4/3 × πr³

This means, volume is proportional to the third power of radius.

∴ % Error of Volume = 3 × % Error of Radius.

∴ % error of volume = 3 × 4 %

∴ Error in volume = 12 %.

Hence, the %error of volume = 12 %.❤️