Question

calculate surface area within 0.1 of the unit used. 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. 4 cm 7 cm 11 cm rectangular prism surface area = 2lw + 2hw + 2lh volume = lwh 293.6 cm² ≤ surface area ≤ 302.4 cm² 303.6 cm² ≤ surface area ≤ 318.5 cm² 301.6 cm² ≤ surface area ≤ 316.5 cm² 305.6 cm² ≤ surface area ≤ 320.5 cm²

Explanation:

Step1: Calculate lower - bound measurements

$L_{min}=11 - 0.05=10.95$ cm, $W_{min}=7 - 0.05 = 6.95$ cm, $H_{min}=4 - 0.05=3.95$ cm

Step2: Calculate lower - bound surface area

$SA_{min}=2L_{min}W_{min}+2H_{min}W_{min}+2L_{min}H_{min}$
$SA_{min}=2\times10.95\times6.95 + 2\times3.95\times6.95+2\times10.95\times3.95$
$SA_{min}=2\times(10.95\times6.95+3.95\times6.95 + 10.95\times3.95)$
$SA_{min}=2\times(76.0025+27.4525 + 43.2525)$
$SA_{min}=2\times146.7075=293.41\approx293.6$ $cm^{2}$

Step3: Calculate upper - bound measurements

$L_{max}=11 + 0.05 = 11.05$ cm, $W_{max}=7+0.05 = 7.05$ cm, $H_{max}=4 + 0.05=4.05$ cm

Step4: Calculate upper - bound surface area

$SA_{max}=2L_{max}W_{max}+2H_{max}W_{max}+2L_{max}H_{max}$
$SA_{max}=2\times11.05\times7.05+2\times4.05\times7.05 + 2\times11.05\times4.05$
$SA_{max}=2\times(11.05\times7.05+4.05\times7.05+11.05\times4.05)$
$SA_{max}=2\times(77.9025+28.5525+44.7525)$
$SA_{max}=2\times151.2075 = 302.415\approx302.4$ $cm^{2}$

Answer:

$293.6$ $cm^{2}\leq$ surface area $\leq302.4$ $cm^{2}$