Question

A circular wire of radius =7.5cm is cut and bent so as to lie along the circumference of a hoop whose radius is 120cm.find the degree the angle which is subtended at the centre of the hoop?

Answer 1

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Answer 2

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A circular wire of radius =7.5cm is cut and bent so as to lie along the circumference of a hoop whose radius is 120cm.find the degree the angle which is subtended at the centre of the hoop?

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$\sf \: Radius \: of \: the \: circular \: wire = 7.5 cm$

$\sf \: It's \: perimeter = 2πr \\ \sf \: = 2 \times \pi \times 7.5 \: cm \\ \sf \: = 15\pi \: cm$

$\sf \: Now, \\ \sf \: For \: circular \: hoop, \\ \sf \: Length = 15π ; Radius = 120 cm$

$\sf \: Let \: the \: angle \: between \: be \: '\theta ' \\ \sf \: radians , using \: \frac{l}{r} = \theta.$

$\sf \frac{15\pi}{120} = \theta \\ \\ \sf \implies \theta = \frac{\pi}{8} \\ \\ \sf \implies\theta = \frac{\pi}{8} \times \frac{180}{\pi} \\ \\ \sf \implies \: 22 \frac{1}{2} \degree \\ \\ \boxed{ \red{ \sf{ \therefore \: \theta \: = \: {22} \degree {30}^{'} }}}$