Question

7 7
B. The length of minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
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Answer 1

Question

• The length of minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

$\bf\underbrace\orange{Answer:}$

Given :-

• The length of minute hand of a clock is 14 cm.

To find :-

• The area swept by the minute hand in 5 minutes.

Formula used :-

${\red\bigstar\: { \boxed{\large{\bold\red{Area_{(Sector)}\:\ = \:\pi r^2 \dfrac{θ}{360} }}}}} \:★$

where,

• r = radius of circle
• θ = sector angle

$\bf\underbrace\orange{Solution:}$

We know,

The minute hand in 60 minutes, subtends an ange of 360°.

So, minute hand in 1 minute, subtends an angle of 6°.

⇛ minute hand in 5 minutes, subtends an angle of 30° at the centre.

Now, Radius of circle, r = 14 cm

Sector angle, θ = 30°.

So, required area of Sector is given by

${\red\bigstar\: { \boxed{\large{\bold\red{Area_{(Sector)}\:\ = \:\pi r^2 \dfrac{θ}{360} }}}}} \:★$

On substituting the values of r = 14 and θ = 30, we get

$\implies \bf \: Area_{(Sector)} = \dfrac{22}{7} \times 14 \times 14 \times \dfrac{30}{360}$

$: \implies \bf \: Area_{(Sector)} =\dfrac{154}{3} \: {cm}^{2}$

$\bf\implies \:Area swept \: by \: the \: minute \: hand \: in \: 5 \: minutes \: = \dfrac{154}{3} \: {cm}^{2}$

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Answer 2

Answer:

length of minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5

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