Blocks of stone are cut to a nominal size of 60cm x 30cm x 15cm, where measurements are correct to the nearest centimeter. Find the range of values of the volumes of a block giving your answer in the form V± pV, where V is the nominal volume and p is the percentage.
each dimension is ±0.5cm
so, figure the min/max range and divide the error by the nominal volume
how do you find the error?
But I get 2 different percentages?
To find the range of values of the volumes of a block, we need to consider the maximum and minimum possible values based on the given measurements.
The nominal volume of the block can be calculated by multiplying the three dimensions together:
V = 60cm * 30cm * 15cm
V = 27000 cm³
Now, let's consider the maximum and minimum values for each dimension based on the given precision of measurements.
For the length:
Maximum possible length = 60cm + 0.5cm (half of the precision value)
Minimum possible length = 60cm - 0.5cm
For the width:
Maximum possible width = 30cm + 0.5cm
Minimum possible width = 30cm - 0.5cm
For the height:
Maximum possible height = 15cm + 0.5cm
Minimum possible height = 15cm - 0.5cm
Now, we can calculate the maximum and minimum volume using these maximum and minimum values for each dimension:
Maximum volume = (60cm + 0.5cm) * (30cm + 0.5cm) * (15cm + 0.5cm)
Minimum volume = (60cm - 0.5cm) * (30cm - 0.5cm) * (15cm - 0.5cm)
Calculating these values, we get:
Maximum volume = 61cm * 30.5cm * 15.5cm = 28810.75 cm³
Minimum volume = 59.5cm * 29.5cm * 14.5cm = 24632.75 cm³
Finally, let's express the range of volumes in the form V ± pV, where V is the nominal volume and p is the percentage:
V ± pV = 27000 cm³ ± (28810.75 cm³ - 24632.75 cm³)
V ± pV = 27000 cm³ ± 418.00 cm³
Therefore, the range of values of the volumes of a block is approximately 27000 cm³ ± 418.00 cm³.