Question

calculate volume within 0.1 of the unit used. use 3.14 for pi. to find the numbers within 0.1 of the unit used, take 0.1 and divide by 2. 0.1/2 is 0.05. take each measurement required in the formula and subtract 0.05 from them. then find the volume using these measurements. next take the measurements required in the formula and add 0.05 to them. take the new measurements and find the volume. your answer will be a range from your lowest volume to your highest volume. round to the nearest hundredth. 12 cm 6 cm 7 cm rectangular prism surface area = 2lw + 2hw + 2lh volume = lwh 494.16 cm³ ≤ volume ≤ 514.00 cm³ 494.16 cm³ ≤ volume ≤ 513.96 cm³ 494.17 cm³ ≤ volume ≤ 513.96 cm³ 494.17 cm³ ≤ volume ≤ 514.00 cm³

Explanation:

Step1: Calculate lower - bound dimensions

$L_{lower}=12 - 0.05=11.95$ cm, $W_{lower}=7 - 0.05 = 6.95$ cm, $H_{lower}=6 - 0.05=5.95$ cm

Step2: Calculate lower - bound volume

$V_{lower}=L_{lower}W_{lower}H_{lower}=11.95\times6.95\times5.95$
$V_{lower}=11.95\times(6.95\times5.95)=11.95\times41.3525\approx494.16$ $cm^{3}$

Step3: Calculate upper - bound dimensions

$L_{upper}=12 + 0.05 = 12.05$ cm, $W_{upper}=7+0.05 = 7.05$ cm, $H_{upper}=6 + 0.05=6.05$ cm

Step4: Calculate upper - bound volume

$V_{upper}=L_{upper}W_{upper}H_{upper}=12.05\times7.05\times6.05$
$V_{upper}=12.05\times(7.05\times6.05)=12.05\times42.6525\approx513.96$ $cm^{3}$

Answer:

$494.16\ cm^{3}\leq volume\leq513.96\ cm^{3}$