to the nearest 20 centimetres, the radius of a circular pond is 220cm.
a) between wat limits must the radius, r cm lie?
b)calculate the smallest possible circumference of the pond.
Hello Mr. Mann:
I read this as, "Rounded to the nearest 20 cm ..."
If we're rounding numbers to the nearest 20, then we're considering numbers like the following.
... 160, 180, 200, 220, 240, 260 ...
The true radius of the pond could be either larger than 220 OR smaller than 220.
So, the real questions are, "How much smaller and still round to 220?" and "How much bigger and still round to 220?".
If we follow the convention when rounding numbers, then we look to the value halfway between 200 and 220 when considering whether to round up to 220, and we look to the value halfway between 220 and 240, when considering whether to round down to 220.
These values are 210 and 230.
In other words, the convention says (at the lower end of the range of possible true values) that if the true radius of the pond is less than 210, then we round down to 200 because those values are closer to 200 than to 220.
If the true radius is 210 or more, then we round up to 220 because those values are closer to 220 than to 200.
If the true radius (at the upper end of the range of possible true values) is less than 230, then we round down to 220 because those values are closer to 220 than to 240.
If the true radius is 230 or more, then we round up to 240 because those values are closer to 240 than to 220.
So, part (a) is really asking you, "What is the lowest value that we could have that requires rounding up to 220?" and "What is the largest value that we could have that requires rounding down to 220?".
Hopefully, I just answered these two questions for you.
(These lowest and largest values are the limits that define the range in which the true radius must lie in this exercise.)
Once we determine the lowest value, we use it to calculate the circumference for part (b).
Cheers,
~ Mark
PS: I should probably also state that I'm assuming that the true radius is a whole number because, if we allow fractional parts of a centimeter, then there is no largest number less than 230.