Question

The minute hand of a clock is root 21cm long. Find the area described by the minute hand between 8Am and 8.25Am.
Plz provide solution....

Answer 1

$\huge\underline\blue{\sf Answer:}$

$\large\red{\boxed{\sf Area(A)=27.5{cm}^{2} }}$

$\huge\underline\blue{\sf Solution:}$

$\large\underline\pink{\sf Given: }$

• Radius (r) =$\sf{\sqrt{21}}$

$\large\underline\pink{\sf To\:Find: }$

• Area described by the minute hand between 8 am and 8.25 am = ?

━━━━━━━━━━━━━━━━━━━━━━━━

We know that ,

$\large{♡}$$\large{\boxed{\sf Area\:of\:Sector(A)={\frac{\theta}{360°}}×πr^{2}}}$

Calculation of $\sf{\theta}$

Angle subtended by minute hand 60 mins= 360°

$\large{\sf 1min={\frac{360}{60}}\implies 6°}$

Therefore ,

$\large{\sf 25min=6°×25 \implies 150° }$

On putting value :

$\large\implies{\sf {\frac{150}{360}}×3.14×\sqrt{21}^2}$

$\large\implies{\sf {\frac{15}{36}}×3.14×21}$

$\large\implies{\sf 27.5{cm}^{2}}$

$\huge\red{♡}$$\large\red{\boxed{\sf Area(A)=27.5{cm}^{2} }}$

Answer 2

$\huge{\boxed{\boxed{\mathfrak{\purple{Answer:-}}}}}$

${\bold{\underline{\underline{Given:-}}}}$

•Radius = √21cm

${\bold{\underline{\underline{To \: find :-}}}}$

• Area= ❓

${\bold{\underline{\underline{Formula \: used:-}}}}$

$\huge\implies\frac {θ}{360°}\times\ πr^2$

Calculate θ :-

Angle subtended by minute clock in 1min➡

$\implies\frac {360°}{60} \\ \\ \implies\ θ =6°\\ \\ \implies\ for 25 min. = 25 \times\ 6° \\ \\ \implies\ θ= 150°$

Now;put values in formula :-

$\implies\ 150/360 \times\ 3.14 \times\ 21 \\ \\ \implies 27.5cm^2$

$\mathbb\red{Thanks..}$