Question

The length of minute hand of a clock is 14 cm. Find the area swept by the minute hand in one minute *​

Answer 1

Hello Mate

The minute hand moves a complete rotation in a minute so we can use the formula (pie)*(radius)^2

[In this case we can say the radius is 14cm]

So just substitute the values in the formula Mate

(3.14)*(196) = 615.44(approx)

Hope this helps

Have a good day mate

Answer 2

Answer:-

The area swept by the minute hand in one minute is 10.26cm²

Step-by-step explanation:-

To Find:-

The area swept by the minute hand ..(?)

Given that,

Lenght of minute hand is 14cm

Now, let's find the angle made by minute hand in 1 minute

$\boxed{ \boxed{ \sf{1 \: minute \: = \: 60 \: seconds}}}$

Therefore,

$\therefore \: \: \sf{ \dfrac{360 \degree}{60 \degree}}$

Dividing 360 and 60 with 6

$\longrightarrow \: \dfrac{60}{10}$

Dividing 60 and 10 with 10

$\longrightarrow \: {6 \degree}$

Now, let's the area swept by minute hand :—

$\bold{Let's \: take \: \pi = \dfrac{22}{7} }$

$\sf{ \longrightarrow \: \dfrac{6}{360} \times \pi {r}^{2}}$

Now, by putting the values,

$\longrightarrow \: \dfrac{6}{360} \times \dfrac{22}{7} \times ( {14})^{2}$

$\longrightarrow \: \dfrac{6}{360} \times \dfrac{22}{7} \times 14 \times 14$

Dividing 7 and 14 with 7

$\longrightarrow \: \dfrac{6}{360} \times 22 \times \: 2 \times 14$

Dividing 6 and 360 with 6

$\longrightarrow \: \dfrac{1}{60} \times 22 \times 2 \times 14$

Dividing 60 and 22 with 2

$\longrightarrow \: \dfrac{1}{30} \times 11 \times 2 \times 14$

Dividing 30 and 14 with 2

$\longrightarrow \: \dfrac{11 \times 2 \times 7}{15}$

$\longrightarrow \: \dfrac{154}{15}$

Therefore, The area swept by the minute hand in one minute is 10.26cm²