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20 August, 09:08

A circular garden has a circumference of 21 pi yards. Lars is digging a straight line along across the garden at a rate of 7 yards per hour. How many hours will it take to dig across

the garden?

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  1. 20 August, 12:47
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    Answer: He took 3 hours to dig across the garden

    Step-by-step explanation: First of all, we calculate the radius of the circular garden. Digging across the garden simply means drawing a line from end to end along the middle of the garden (in other words, the diameter).

    The circumference has been given as 21pi. If the circumference is calculated as

    Circumference = 2Pi x r, then

    21Pi = 2Pi x r

    By cross multiplication we now have

    (21Pi/2Pi) = r

    21/2 = r

    10.5 = r

    If the radius has been identified as 10.5 yards, then the diameter can be derived as radius times 2

    Diameter = 10.5 x 2

    Diameter = 21 yards

    However, he is digging at a rate of 7 yards per hour, which means by the time he has dug 21 yards he has spent;

    7 yds = 1 hr

    (7 x 3 = 21 yds) = 1 x 3 hrs

    21 yds = 1 x 3 hrs

    21 yds = 3 hrs

    Therefore he took 3 hours to dig across the garden.
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