Question

The minute hand of a clock is 8 cm long. Find the area swept by the minute hand between 8.30 a.m, and 9.05 a.m.
A.\[177\dfrac{1}{3}c{{m}^{2}}\]
B.\[107\dfrac{1}{3}c{{m}^{2}}\]
C.\[217\dfrac{1}{3}c{{m}^{2}}\]
D. None of these

Answer 1

Hint: To solve this question, we have to get the minute moved by the minute hand and then convert the value in angles as we know 60 minutes = \[360{}^\circ \]. Then we have to find the area covered by the minute hand using the formula Area of sector = \[\dfrac{\theta }{360{}^\circ }\times \pi \times {{r}^{2}}\] to get the required value.

Complete step-by-step solution:
We are given that the minute hand of the clock is 8 cm long.
We are supposed to find the area swept by the minute hand between 8.30 a.m and 9.05 a.m.

So, the minutes between 8.30 a.m and 9.05 a.m . = 35 minutes
We know that, 60 minutes = \[360{}^\circ \]
From this we can get 1 minute = \[\dfrac{360}{60}\] = \[6{}^\circ \]
So we can write 35 minutes as follows,
\[\Rightarrow \] 35 minutes = \[35\times 6{}^\circ \] = \[210{}^\circ \]
We have the formula for area of sector = \[\dfrac{\theta }{360{}^\circ }\times \pi \times {{r}^{2}}\]
On substitute the values obtained from the question we get,
Area of sector = \[\dfrac{210{}^\circ }{360{}^\circ }\times \pi \times {{\left( 8 \right)}^{2}}\] = \[177\dfrac{1}{3}c{{m}^{2}}\]
Hence the area swept by minute hand is \[177\dfrac{1}{3}c{{m}^{2}}\]
So option A is correct.

Note: It is important for students to know that the values of minute to degree conversion to convert the value in the question and also the student should be aware of the formula to find the area of the sector.