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Abel wants to build a backyard patio using bricks. The diagram below demonstrates the shape of the patio. The patio will be fenced and paved. Abel will also add a round 12-inch-high pit, built with bricks in one of the corners of the patio. The diameter of the fire pit is 91,44 cm.
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Step-by-step solution
16 steps2.1.1
Identify the lengths of all sides of the patio from the diagram.
The lengths are , , , and .
Add the lengths of all sides to find the total length of fencing (perimeter).
Calculate the sum.
The total length of the fencing required is .
2.1.2
Calculate the radius () of the fire pit from its diameter.
Given diameter () = .
Substitute the radius and given height () into the lateral surface area formula.
Calculate the lateral surface area.
Rounding to two decimal places:
The lateral surface area of the fire pit is .
2.2.1
The map scale represents the ratio of a distance on the map to the corresponding actual distance in reality.2.2.2
Divide the first part of the ratio (25) by 25 to get 1.
Divide the second part of the ratio (10 000 000) by 25.
The map scale as a unit ratio is .
2.2.3
Calculate the actual distance in cm using the unit ratio from 2.2.2 (1 cm on map = 400 000 cm in reality).
Given map distance = .
Convert the actual distance from cm to km.
(Note: ).
Calculate the actual distance in km.
The actual distance between the two towns is .
2.2.4
Convert Phumeza's estimated distance from cm to km.
Estimated distance = .
Calculate the travel time using the formula Time = Distance/Speed.
Given speed = .
Convert the travel time from hours to minutes.
Calculate the arrival time by adding the travel time to the departure time (08:00 a.m.).
Compare the arrival time with the desired arrival time (before 09:00 a.m.).
Since 08:27 a.m. is before 09:00 a.m., Phumeza's mother will have the possibility of arriving before 09:00 a.m.
Phumeza's mother will arrive at , which is before 09:00 a.m.
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