Question

Q.2 If the error in measurement of radius of a sphere is 1.5%, then error in the
determination of surface area of the sphere will be
Choose answer:
O
1.5%
2%
3%
4.5%​

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Let radius of sphere = R
• Error in radius ${\sf \left(\dfrac{\Delta R}{R}\right)}$=1.5%

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Error in surface area of sphere

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❏ Surface Area of Sphere

$\color{violet}\underline{\boxed{\sf A=4πR^2}}$

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❏ Error in Radius

$\color{orange}\implies{\sf \dfrac{\Delta R}{R}=1.5\% = 0.015 }$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━

❏ Error in Surface Area

$\implies{\sf \dfrac{\Delta A}{A}=\dfrac{4π×2R×\Delta R}{4πR^2}}$

$\implies{\sf 2×\dfrac{\Delta R}{R}}$

$\implies{\sf 2×0.15}$

$\implies{\sf 0.03}$

$\implies{\sf 0.03×100}$

$\color{red}\implies{\sf \dfrac{\Delta A}{A}=3\%}$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Option (3) 3%

Answer 2

Given: Error in the radius of a sphere=

$\frac{ΔR}{R}$ =1.5%

To find: Error in the surface area of a sphere

Finding the surface area of the sphere:

Let the radius of the sphere = R

We know, that the Surface area of the sphere= $4πr²$

It is given that the Error in the radius of a sphere= 1.5%

Therefore, Error in the Surface area=

Error in the Surface area= $\frac{A}{ΔA} = \frac{4\pi \times 2R \times ΔR}{4\pi {R}^{2} }$

Error in the Surface area= $\frac{A}{ΔA} = \frac{4\pi \times 2R \times ΔR}{4\pi {R}^{2} }$$= 2 \times \frac{ΔR}{R}$

= 2 × 0.15

= 0.03

= 0.03 × 100

= 3%

Hence, the correct answer among all the options is 3%.

(#SPJ2)