Author name: Gulam Hamza

The correct answer is: 22 cm, 231 cm² Explanation: Let AB be the given arc subtending an angle of 60° at the centre. Here, r = 21cm and θ = 60° $\displaystyle \begin{array}{l}\text{Length of the arc ABC}=\dfrac{{2\pi r\theta {}^\circ }}{{360{}^\circ }}cm\=\left( {2\times \dfrac{{22}}{7}\times 21\times \dfrac{{60{}^\circ }}{{360{}^\circ }}} \right)cm=\text{ }22cm\\text{Area of the sector OACBO}=\dfrac{{\pi {{r}^{2}}\theta {}^\circ }}{{360{}^\circ […]

The correct answer is: 693 cm² Explanation: Since the ribs are equally spaced, so the angle made by two consecutive ribs at the centre =(${\displaystyle {\displaystyle \frac{360}{8}}}$​)° = 45° Area between two consecutive ribs = area of a sector of a circle with r = 42 cm and θ = 45° =(${\displaystyle {\displaystyle \frac{45}{3600}}}$ × ${\displaystyle {\displaystyle \frac{22}{7}}}$ ​× 42

The correct answer is: 9.625 cm² Explanation: Area of shaded region = ${\displaystyle {\displaystyle \frac{22\times 30°}{7\times 360°}}}$  × (7² − 3.5²) = 9.625cm²

The correct answer is: 17: 21 Explanation: We known that ratio of areas of two similar triangles is equal to the ratio of square of their corresponding heights. ${\displaystyle {\displaystyle \frac{ar(△ABC)}{ar.(△DEF)}}}$ = ${\displaystyle {\displaystyle \frac{(4)²}{(9)²}}}$ =  ${\displaystyle {\displaystyle \frac{16}{81}}}$ ​