GATE Overflow Test Series | Quantitative Aptitude | Test 1 | Question: 8

Question

A sector has radius $17\,\text{cm}$ and angle $30^\circ.$ Its area equals _______

• A. $75.66\,\text{cm}^{2}$
• B. $75.42\,\text{cm}^{2}$
• C. $75.96\,\text{cm}^{2}$
• D. $74.62\,\text{cm}^{2}$

Answer 1

If the angle $\theta$ is in degrees, then the area of sector is $\dfrac{\theta}{360^{\circ}}$
 of the circle. Since the area of the circle is $\pi r^{2},$ the area of sector is

$\dfrac{\theta}{360^{\circ}} \times \pi r^2.$

If $\theta$ is in radians, then the area of sector is $\dfrac{\theta}{2\pi}$ of the circle, and hence the area of sector is $\dfrac{\theta}{2\pi} \times \pi r^2 =\dfrac{1}{2} r^2 \theta.$

Given that, sector radius $r = 17\,\text{cm}$

Required area $A = \dfrac{\theta}{360^{\circ}} \times \pi r^{2}$

$\implies A = \dfrac{30^{\circ}}{360^{\circ}} \times \pi \times 17^{2}$

$\implies A = \dfrac{\pi \times 289}{12}$

$\implies A = 75.66\,\text{cm}^{2}.$

 So, the correct answer is $(A).$

Comments

gatecse What value of pi is taken in the solution because if we take pi = 3.14 then we get answer = 3.14 * 289 / 12 = 72.621666667 and we use calculator value of pi then we get answer = 75.6600. So isn't option D more correct?

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Option D is 74 and not 75.

Always one should use the most precise value of any variable. 3.14 or 22/7 can be used only when some inaccuracy is acceptable (like when options are far apart). But the final digit here must be 6 and not 9. Just fixed it.

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Thanks 😊

I totally misread the options and then went to change value of pi to 3.14.