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A cricket stadium is called an "Oval" due to its unique shape. Use the diagram below to answer the questions that follow. 1.1 Calculate the area of the pitch. 1.2 Calculate the area of the oval to two decimals. 1.3 Calculate the area of the grass only.
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5 stepsCalculate the area of the pitch (1.1.1)
The pitch is a rectangle with a length of and a width of .
The area of the pitch is .
Calculate the area of the oval (1.1.2)
The oval is a stadium shape, composed of a rectangular section and two semi-circular ends.
The length of the rectangular section is .
The radius of the semi-circular ends is .
The width of the rectangular section is equal to the diameter of the semi-circles, which is .Area of the rectangular part of the oval:
Area of the two semi-circular ends (which form one full circle):
Total area of the oval:
Rounding to two decimal places:
The area of the oval is .Calculate the area of the grass only (1.1.3)
The area of the grass is the area of the oval minus the area of the pitch.
Rounding to two decimal places:
The area of the grass only is .Calculate the average number of seats in one block (1.2.1)
The stadium has a capacity of 28000 seats arranged in 8 blocks.
On average, there are in one block.
Verify the caretaker's claim about the number of rows (1.2.2)
Each row of seats needs a height of . The stadium height is . The caretaker claims there are 43 rows.
First, convert the height per row to meters:Calculate the total height required for 43 rows:
Compare this to the stadium height:
The calculated height required for 43 rows is , which is greater than the stadium's height of .
Therefore, the caretaker's claim is .
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