Do You Know How to Find the Area of a Circular Sector?

By Team Aakash Byju's | 16th December 2022

A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°.

[{"selector":"#anim-77d1f9d8-e7ec-4d91-8e5a-e25a602173df","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-25d28d0d-eb7a-4137-8ac1-84e45e443be5","keyframes":{"transform":["translate3d(-118.21191%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-e879dcee-267d-46f1-89c8-864ca736be30","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-67ec6e2c-b429-4ec6-9fe8-5267eb1bd923","keyframes":{"transform":["translate3d(-117.79935%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] Find the total area cleaned at each sweep of the blades.

The total area cleaned by both wipers is 1254.96 cm.

[{"selector":"#anim-5ba1fe7e-9aa3-4079-b387-9142b2bffe2f","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-d734e1dd-9841-446e-b53e-05ca660ce422","keyframes":{"transform":["translate3d(-118.21191%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-e91cc351-9473-4043-a315-f8310b1108e4","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-2ff92145-ea21-44f8-a673-72480abeac14","keyframes":{"transform":["translate3d(-1236.36272%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-9a62881c-1e75-4e70-8848-5f68993b52e4","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-2cac6049-6ef1-465e-baaa-1b17b1be7bd5","keyframes":{"transform":["translate3d(-117.82179%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] Continue to see the calculation step-by-step. 2

[{"selector":"#anim-103e76b8-0080-424a-8452-2fea84b6e607 [data-leaf-element=\"true\"]","keyframes":{"transform":["translate3d(0%, 0, 0) translate(25%, 0%) scale(1.5)","translate3d(0%, 0, 0) translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.14,.34,.47,.9)","fill":"forwards"}] Book A Trial Class

Assume that the wiper represents the radius of the circle, i.e., 25 cm and it forms an angle of 115° at the centre of the circle.

[{"selector":"#anim-289d6b9a-cab2-498d-a1f3-012333efde83","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-dc2aced8-f16d-4a03-bcbf-549fea5eb8b0","keyframes":{"transform":["translate3d(-117.46031%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}]

Since both wipers do not overlap, we can say that the total area cleaned by both wipers is twice the area cleaned by either of them.

[{"selector":"#anim-f967b143-a985-44db-8ba8-7a088cb94ec5","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-99d01369-9072-4927-bcd2-2cbb6e72d1d1","keyframes":{"transform":["translate3d(-117.46031%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}]

The area cleaned by one wiper is the area of the sector of a circle with a radius of 25 cm at an angle of 115°. So the formula is

[{"selector":"#anim-d81326f7-bb7a-4e78-8c49-e5224dce3ea4","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-b9fe55ba-e825-4fd0-9ec9-75e7d304ef73","keyframes":{"transform":["translate3d(-117.6282%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] Area of sector = 0 360 0 × πr 2

=> Area = 115 360 0 0 × 22 7 × 25 2 => Area = 627.48 cm (Rounded to 2 decimal places) 2

So, the area cleaned by one wiper is 627.48 cm , but the area covered by both wipers is:

[{"selector":"#anim-9b2639c6-9161-441e-9af3-e6213102bf92","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-bd52e6ea-b86e-4723-af59-bd8e36572a45","keyframes":{"transform":["translate3d(-118.21191%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-7348e755-cba6-49d2-a064-8ec851f698f6","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-cee6b78b-79eb-417a-b6f9-1572226c17d1","keyframes":{"transform":["translate3d(-1186.36281%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] 2 Total area cleaned = 2×627.48 = 1254.96 cm 2

[{"selector":"#anim-a9485907-e5b2-4489-84c1-31ccbb8d3b34 [data-leaf-element=\"true\"]","keyframes":{"transform":["translate3d(0%, 0, 0) translate(25%, 0%) scale(1.5)","translate3d(0%, 0, 0) translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.14,.34,.47,.9)","fill":"forwards"}] Download Aakash App Now

Read More Stories

[{"selector":"#anim-a1eda4e3-f94b-46c6-874f-3ff96e0761f8","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-34dad639-fc58-48c1-8102-8147c00ce1d0","keyframes":{"transform":["translate3d(-133.7931%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-dad1e924-b41e-435b-b2f3-16ca943f6142","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-f351f8a9-f6c2-4bec-8ddc-01b756d4df65","keyframes":{"transform":["translate3d(-133.7931%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-c4832e67-f964-4c95-82b9-07e5e48567cc","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-e2ca7155-bfe3-41e6-a5dc-5dd932880f01","keyframes":{"transform":["translate3d(128.83434%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-16c94a26-81fe-4402-ba55-439d920987b5","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-4dff6d03-4538-4a4c-9a67-e9128e1c86a8","keyframes":{"transform":["translate3d(-141.37933%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-99c45b8c-d7d9-4e54-a179-e4cecfc2ba54","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-954580ec-9c39-4882-8b03-d61146a75cc6","keyframes":{"transform":["translate3d(-141.37933%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-04d44a08-a28a-43a3-900c-aaf7d3b3fece","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-93af4a71-e9d5-4372-b95c-9cacf5fe97d0","keyframes":{"transform":["translate3d(122.08588%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-b05674ee-6445-4ca1-9f35-86059a2ed06d","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-4a81e043-17d6-4abd-954f-5386c7dda58f","keyframes":{"transform":["translate3d(129.37501%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-156e5d99-b35f-4388-a0c6-43916ef7743b","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-4618997a-d9d3-439f-a7e3-461fa80af8eb","keyframes":{"transform":["translate3d(119.87952%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] What Is a Surd in Maths? Explained With Example Obtuse-Angled Triangle Notes for NCERT Maths Revision