The shaded area shows a beach. AD and BC are circular arcs, centre O.
OB = 160m, OD = 100m and an angle AOD = 95°
a) Calculate the area of the beach ABCD in square metres.
b) The beach area is covered in sand to a depth of 1.8 m.
Calculate the volume of the sand in cubic metres.
Please help me anyone it's very important for me and I'll be thankful to you.
Answers
Given : shaded area shows a beach. AD and BC are circular arcs, centre O. OB = 160m, OD = 100m and an angle AOD = 95°
The beach area is covered in sand to a depth of 1.8 m.
To Find :
a) area of the beach ABCD in square metres.
b) volume of the sand in cubic metres.
Solution:
area of the beach ABCD = Area of sector OBC - Area of sector OAD
Area of sector OBC = (95/360)π160²
Area of sector OAD = (95/360)π100²
area of the beach ABCD = (95/360)π160² - (95/360)π100²
= (95/360)π ( 160 + 100)(160 - 100)
= (95/360)π 260 * 60
= (95/6)π 260
π = 22/7
= 12,938 m²
The beach area is covered in sand to a depth of 1.8 m
Volume of sand = 12,938 * 1.8
= 23,288.4 m³
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