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r = 3.5 cm; l = 8.2 cm. Curved surface area = \(\pi rl\) = \(\frac{22}{7} \times \frac{7}{2} \times \frac{41}{5}\) = 90.2 cm\(^2\)

Circumference of circle = 2πr = 2 x 3.14 x 4 = 25.1cm 360o = 25.1cm 70o = 25.1/360 x 70 = 4.89

Reflex POR = 2PQR Reflex PQR = 360o - 114o = 246o PQR = 246/2 = 123o

Tan 69.7 = 40/h h = 40/tan 69.7 = 40/2.703 h = 14.79 = 14.8

In the 2nd Quadrant, SINE is the only Positive. Where \theta is 30 for the first quadrant and 150 in the 2nd quadrant, which makes COSINE negative Sin \theta = \(\frac{1}{2}\) \theta = Sin\(^{-1}(\frac{1}{2}\)) = 30º which is positive in the first quadrant Sin 30 = Sin 150, i.e, (180 - 30), which is also positive in the second quadrant. BUT Cos \theta = -\(\frac{\sqrt{3}}{2}\) \theta = Cos\(^{-1}\)(-\(\frac{\sqrt{3}}{2}\)) = 150º which is in the second quadrant but negative Hence, \theta = 150º

80o = 2 x 5x(angle at the center) =80o = 10x; x = 80o/10 = 8o

A regular has all sides and all angles equal. If each interior angle is 140^\circ each exterior angle must be 180^\circ - 140^\circ = 40^\circ The number of sides must be \(\frac{360^o}{40^o}\) = 9 sides hence 2k + 1 = 9 2k = 9 - 1 8 = 2k k = \(\frac{8}{2}\) = 4

PR\(^2\) + QS\(^2\) = kPQ\(^2\) SQ\(^2\) = SR\(^2\) + RQ\(^2\) PR\(^2\) + SQ\(^2\) = PQ\(^2\) + SR\(^2\) + 2RQ\(^2\) = 2PQ\(^2\) + 2RQ\(^2\) = 4PQ\(^2\) ∴ K = 4

Y \(\to\) 30^\circ X \(\to\) 120^\circ Z \(\to\) 30^\circ \(\frac{3}{\text{sin 30}}\) = \(\frac{YZ}{\text{sin 120}}\) YZ = \(\frac{3\times \sin 120}{\sin 30}\) \(3 \times \frac{\sqrt{3}}{2} \times 2 = 3\sqrt{3}\)

13 = 52 1 = \(\frac{52}{13}\) = 4 5 + 12 + 13 = 30 Total perimeter = 30 x 4 = 120cm

x = 10 cot35o - 10 cot55o = 10(cot35o - cot55o)

4 sin2x - 3 = 0 sin2x = \(\frac{3}{4}\) Sin x = \(\pm\) \(\sqrt{\frac{3}{4}}\) = \(\pm\) \(\sqrt{\frac{3}{4}}\) = 60o

Total floor area = 720 x 420 Area of one tile = 30 x 30 No. of tile required = \(\frac{720 \times 420}{30 \times 30}\) = 24 x 14 = 336 tiles