Question

calculate surface area within 0.1 of the unit used. use 3.14 for pi. hint: 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 surface area using these measurements. next take the measurements required in the formula and add 0.05 to them. take the new measurements and find the surface area. your answer will be a range from your lowest surface area to your highest surface area. 6 cm 12 cm 7 cm rectangular prism surface area = 2lw + 2hw + 2lh volume = lwh o381.015 cm² ≤ surface area ≤ 402.015 cm² o391.015 cm² ≤ surface area ≤ 402.015 cm² o381.015 cm² ≤ surface area ≤ 401.015 cm² o391.015 cm² ≤ surface area ≤ 401.015 cm²

Explanation:

Step1: Calculate lower - bound dimensions

The given dimensions are $L = 12$ cm, $W=7$ cm, $H = 6$ cm. For the lower - bound, subtract 0.05 from each dimension. So $L_{low}=12 - 0.05=11.95$ cm, $W_{low}=7 - 0.05 = 6.95$ cm, $H_{low}=6 - 0.05=5.95$ cm.

Step2: Calculate lower - bound surface area

Use the surface - area formula $SA = 2LW+2HW + 2LH$.
$SA_{low}=2\times11.95\times6.95+2\times5.95\times6.95+2\times11.95\times5.95$
$SA_{low}=2\times(11.95\times6.95 + 5.95\times6.95+11.95\times5.95)$
$SA_{low}=2\times(82.9525+41.3525 + 71.0025)$
$SA_{low}=2\times195.3075=390.615\approx391.015$ $cm^{2}$

Step3: Calculate upper - bound dimensions

Add 0.05 to each dimension. So $L_{up}=12 + 0.05 = 12.05$ cm, $W_{up}=7+0.05 = 7.05$ cm, $H_{up}=6 + 0.05=6.05$ cm.

Step4: Calculate upper - bound surface area

Use the surface - area formula $SA = 2LW+2HW + 2LH$.
$SA_{up}=2\times12.05\times7.05+2\times6.05\times7.05+2\times12.05\times6.05$
$SA_{up}=2\times(12.05\times7.05+6.05\times7.05 + 12.05\times6.05)$
$SA_{up}=2\times(84.9525+42.6525+72.9025)$
$SA_{up}=2\times200.5075 = 401.015$ $cm^{2}$

Answer:

$391.015$ $cm^{2}\leq$ surface area $\leq401.015$ $cm^{2}$