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Q.

An umbrella has 8 ribs, which are equally spaced. Assuming the umbrella to be a flat circle of radius 56 cm. Find the area between the two consecutive ribs.


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a

https://lh6.googleusercontent.com/WFDCL_pLq9lyu8MH74f6oOgrcRFNQ0L7rBbqKu4d0mPMHuRlnoBzuX32NEa-sC1YMLkrOKFxT8bL9LXjjv0c_M1ZRjjuFNls5IgizIHFbq8a6H3g48Atzh5h0ciw9-TujiHNKrsXb-4VU6szXUpqUg

b

https://lh4.googleusercontent.com/6CBRtqyW4xaWp31QRaovkUE7h6kZg_hrN0j4W_K7n2z4PssyDk1Uyu-Fz_Q1-zpQkGJPZJJM_WLP8DoFStP_9iIEyM--mJNGw1N3BiFQUzD88DGCLjc3UxyB9J1q8yGFfI2ks8iapQMUQcZ0TFz-vA

c

https://lh4.googleusercontent.com/ONydjE2GlkjBs-0ZnzMxSimt4eN8jDKj9W7ZuSrdKMtlP265Y3bwAQpKMPUyea29tretrkUtr5XP8bKJG2Zudxx5D6I2OSHCKI38uIFMkjKTT_Cg6pRDXw_YsDwj5Qy2lGD4Pw3hjTlH3OTasay0oQ

d

https://lh6.googleusercontent.com/lG6FQPtGZyr6F0y64LNrMWxzuPeRowmS_zeWAHXjbcS3XOnRSIkYhux3_xcPCUVK73EMuD3LzijRc0YLpsBYWX7JtJC6fy-FihXwnudYoXJ4I91b84TBMI_V3i1lZ-wJVpokenUv6heQYWaxRfU5tg

answer is A.

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Detailed Solution

Concept-
Here, we will first apply the formula https://lh3.googleusercontent.com/83-KAnNr3ypWe8wgyo0ljSzWVDW107VDNnaqKINyYUPt5Y9-wsfngoHvmTrMrBXOXrvKqjFUMmW8PSBUs4ISDTk_RBvSUNEMthWR-wjrlQmWjEeAwJ-6IuUEGvD2DDlWOFeXvf9Lxr9wHPBBzHR_3Ato determine the area of the rib, where the area of the umbrella is equal to the area of the circle. Then, to determine the area of the umbrella, we will use the formula for the area of a circle, https://lh4.googleusercontent.com/wI_39JU3obD94PTJstxTVqNkhIMY0vP7SUafK3ZdpdBS_FlXYN1MkwP6XnsJ-eHitgypC0-GlTg2Bld5q4Z7TandKVZGO_1mLG9uvH5ULVRdPEqe9BZJCOhdxLycGPX-yLSwGVI3eAU7X2NrKr9gxg, where r is the radius of the circle.
Using the following formula, the area of the rib is determined =  https://lh3.googleusercontent.com/83-KAnNr3ypWe8wgyo0ljSzWVDW107VDNnaqKINyYUPt5Y9-wsfngoHvmTrMrBXOXrvKqjFUMmW8PSBUs4ISDTk_RBvSUNEMthWR-wjrlQmWjEeAwJ-6IuUEGvD2DDlWOFeXvf9Lxr9wHPBBzHR_3AGiven radius r = 45cm
Area
 https://lh4.googleusercontent.com/ciJwBhxvkImA8YxuSIRe2Owqk76-r68doykV3vPOmNtOsyl8orA676mtsO7cVyMTffEbaT8-Jw_cmhN0DdXD5JgV9QplqzFHXHcpR-EYwkYxW0hhHhkYaxQ5_0c-VFyY9iM7RBj0kKu0wgpp-gRMVgHence, the required area = https://lh3.googleusercontent.com/83-KAnNr3ypWe8wgyo0ljSzWVDW107VDNnaqKINyYUPt5Y9-wsfngoHvmTrMrBXOXrvKqjFUMmW8PSBUs4ISDTk_RBvSUNEMthWR-wjrlQmWjEeAwJ-6IuUEGvD2DDlWOFeXvf9Lxr9wHPBBzHR_3Ahttps://lh6.googleusercontent.com/2pGzy-7ifwbVfHW065vg6mbT8-WDa38zlP8pdJqqEJnHX_exyspT-Sb0UNULw_lSfz6NcSY8xUe7Sp-7dVJV94fZ7lYPVDLR0pUI82DOihR04CrhYiIoSuPy9aQ0Bu2b7CgvdU1JckH90eB4_x-DWQHence, the correct answer is option 1) https://lh6.googleusercontent.com/WFDCL_pLq9lyu8MH74f6oOgrcRFNQ0L7rBbqKu4d0mPMHuRlnoBzuX32NEa-sC1YMLkrOKFxT8bL9LXjjv0c_M1ZRjjuFNls5IgizIHFbq8a6H3g48Atzh5h0ciw9-TujiHNKrsXb-4VU6szXUpqUg 
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