Question

UPPER AND LOWER BOUNDS - PLEASE HELP!

1. zoe weighs 62kg, correct to the nearest kg. write down the lower bound for zoe's weight.
2. the length of line AB=8.3cm, correct to 2 significant figures. write down the upper bound for the length of AB.
3. Anu weighs 83kg, correct to the nearest half kilogram. write down the upper bound for Anu's weight.
4. the length of line CD=27cm, correct to the nearest 0.5cm. write down the lower bound for the length of CD.
5. correct to the nearest mm, the length of a side of a regular hexagon is 3.6cm. calculate the upper bound for the perimeter of the hexagon.
6. the perimeter of a square is 24cm, correct to the nearest half cm. work out the lower bound for the length of a side.
7. correct to 1 significant figure, the area of a rectangle is 80cm^2. correct to 2 significant figures, the length of the rectangle is 12cm. calculate the upper bound for the width.
8. correct to 2 significant figures the area of a sqaure is 230cm^2. calculate the lower bound for the perimeter of the square.

Answer 1

Qn. 1
Lower bound for Zoe's weight = 62 - (1/2) = 62 - 0.5 = 61.5 kg

Qn. 2
Upper bound for length AB = 8.3+ (0.1/2) = 8.3+0.05 = 8.35 cm

Qn. 3
Upper bound for Anu's wight = 83+(0.5/2) = 83+0.25 = 83.25 kg

Qn. 4
Lower bound for length CD = 27-(0.5/2) = 27-0.25 = 26.75 cm

Qn. 5
Upper bound for sides of the hexagon = 3.6+(0.1/2) = 3.6+0.05 = 3.65 cm
Upper bound for the perimeter = upper bound for the sides*6 = 3.65*6 = 21.9 cm

Qn. 6
Perimeter = 4*length => side = Perimeter/4 = 24/4 = 6
Bound = 0.5/4 = 0.125
Lower bound of the length = 6-0.125 = 5.875 cm

Qn. 7
For the area,
Upper bound = 80+(10/2) 80+5 = 85 cm^2
For the length
Upper bound = 12+(1/2) = 12+0.5 = 12.5

Then, upper bound for the width = Upper bound for the area/upper bound for the length = 85/12.5 = 6.8 cm

Qn. 8
Lower bound for the area = 230-(1/2) = 230-0.5 = 229.5 cm^2
Lower bound for the sides of the square = Sqrt(Lower bound of the area) = Sqrt (229.5) = 15.15
Then,
Lower bound of perimeter = 4(Length) = 4*15.15 = 60.6 cm