algebra problem

Question

13.Suppose Josephine measures the dimensions of the sides of a rectangular box to the nearest

mm and finds 1103 mm, 397 mm and x mm. In order to estimate the volume of the box, she

rounds each length to the nearest centimeter before calculating the volume. Using this method,

she estimated the volume to be 88,000 cm^3. What is the maximum possible value of x?

Answer 1

Length = 1103 mm = 110.3 cm (since 10 mm=1 cm) = 110 cm ( rounding to nearest centimetre as .3 < .5)

Breadth = 397 mm = 39.7 cm =40 cm (rounding to nearest centimetre as .7> .5)

Height = ?

Volume = 88000 cm^∧3

Volume = Length ∗ Breadth ∗ Height

88000 = 110 ∗ 40 ∗ X

X = 8800/ (110 ∗ 40) = 20 cm =200 mm

Answer 2

1103*397*x = 88000

x = 0.2 approximately