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Question
homework rectangular prism volume = lwh sa = 2lw + 2lh+2wh 352 = 30 2cm 9cm 3cm 4m 4m 12m 70mm 110mm 20mm cube volume = s^3 surface area sa = 6s^2 6cm 30mm 8m 5cm geometry - volume and surface area
Step1: Calculate volume and surface - area of rectangular prisms
First rectangular prism:
Given $L = 3$cm, $W = 5$cm, $H = 2$cm.
Volume $V_1 = L\times W\times H=3\times5\times2 = 30$ $cm^3$.
Surface - area $SA_1=2LW + 2LH+2WH=2\times3\times5+2\times3\times2+2\times5\times2=30 + 12+20 = 62$ $cm^2$.
Second rectangular prism:
Given $L = 9$cm, $W = 3$cm, $H = 2$cm.
Volume $V_2 = L\times W\times H=9\times3\times2 = 54$ $cm^3$.
Surface - area $SA_2=2LW + 2LH+2WH=2\times9\times3+2\times9\times2+2\times3\times2=54 + 36+12 = 102$ $cm^2$.
Third rectangular prism:
Given $L = 12$m, $W = 4$m, $H = 4$m.
Volume $V_3 = L\times W\times H=12\times4\times4 = 192$ $m^3$.
Surface - area $SA_3=2LW + 2LH+2WH=2\times12\times4+2\times12\times4+2\times4\times4=96 + 96+32 = 224$ $m^2$.
Fourth rectangular prism:
Given $L = 110$mm, $W = 20$mm, $H = 70$mm.
Volume $V_4 = L\times W\times H=110\times20\times70 = 154000$ $mm^3$.
Surface - area $SA_4=2LW + 2LH+2WH=2\times110\times20+2\times110\times70+2\times20\times70=4400+15400 + 2800=22600$ $mm^2$.
Step2: Calculate volume and surface - area of cubes
First cube:
Given $S = 6$cm.
Volume $V_5=S^3=6^3 = 216$ $cm^3$.
Surface - area $SA_5 = 6S^2=6\times6^2=6\times36 = 216$ $cm^2$.
Second cube:
Given $S = 30$mm.
Volume $V_6=S^3=30^3 = 27000$ $mm^3$.
Surface - area $SA_6 = 6S^2=6\times30^2=6\times900 = 5400$ $mm^2$.
Third cube:
Given $S = 8$m.
Volume $V_7=S^3=8^3 = 512$ $m^3$.
Surface - area $SA_7 = 6S^2=6\times8^2=6\times64 = 384$ $m^2$.
Fourth cube:
Given $S = 5$cm.
Volume $V_8=S^3=5^3 = 125$ $cm^3$.
Surface - area $SA_8 = 6S^2=6\times5^2=6\times25 = 150$ $cm^2$.
| Shape | Dimensions | Volume | Surface Area |
|---|---|---|---|
| Rectangular Prism | $L = 9$cm, $W = 3$cm, $H = 2$cm | $54$ $cm^3$ | $102$ $cm^2$ |
| Rectangular Prism | $L = 12$m, $W = 4$m, $H = 4$m | $192$ $m^3$ | $224$ $m^2$ |
| Rectangular Prism | $L = 110$mm, $W = 20$mm, $H = 70$mm | $154000$ $mm^3$ | $22600$ $mm^2$ |
| Cube | $S = 6$cm | $216$ $cm^3$ | $216$ $cm^2$ |
| Cube | $S = 30$mm | $27000$ $mm^3$ | $5400$ $mm^2$ |
| Cube | $S = 8$m | $512$ $m^3$ | $384$ $m^2$ |
| Cube | $S = 5$cm | $125$ $cm^3$ | $150$ $cm^2$ |
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Step1: Calculate volume and surface - area of rectangular prisms
First rectangular prism:
Given $L = 3$cm, $W = 5$cm, $H = 2$cm.
Volume $V_1 = L\times W\times H=3\times5\times2 = 30$ $cm^3$.
Surface - area $SA_1=2LW + 2LH+2WH=2\times3\times5+2\times3\times2+2\times5\times2=30 + 12+20 = 62$ $cm^2$.
Second rectangular prism:
Given $L = 9$cm, $W = 3$cm, $H = 2$cm.
Volume $V_2 = L\times W\times H=9\times3\times2 = 54$ $cm^3$.
Surface - area $SA_2=2LW + 2LH+2WH=2\times9\times3+2\times9\times2+2\times3\times2=54 + 36+12 = 102$ $cm^2$.
Third rectangular prism:
Given $L = 12$m, $W = 4$m, $H = 4$m.
Volume $V_3 = L\times W\times H=12\times4\times4 = 192$ $m^3$.
Surface - area $SA_3=2LW + 2LH+2WH=2\times12\times4+2\times12\times4+2\times4\times4=96 + 96+32 = 224$ $m^2$.
Fourth rectangular prism:
Given $L = 110$mm, $W = 20$mm, $H = 70$mm.
Volume $V_4 = L\times W\times H=110\times20\times70 = 154000$ $mm^3$.
Surface - area $SA_4=2LW + 2LH+2WH=2\times110\times20+2\times110\times70+2\times20\times70=4400+15400 + 2800=22600$ $mm^2$.
Step2: Calculate volume and surface - area of cubes
First cube:
Given $S = 6$cm.
Volume $V_5=S^3=6^3 = 216$ $cm^3$.
Surface - area $SA_5 = 6S^2=6\times6^2=6\times36 = 216$ $cm^2$.
Second cube:
Given $S = 30$mm.
Volume $V_6=S^3=30^3 = 27000$ $mm^3$.
Surface - area $SA_6 = 6S^2=6\times30^2=6\times900 = 5400$ $mm^2$.
Third cube:
Given $S = 8$m.
Volume $V_7=S^3=8^3 = 512$ $m^3$.
Surface - area $SA_7 = 6S^2=6\times8^2=6\times64 = 384$ $m^2$.
Fourth cube:
Given $S = 5$cm.
Volume $V_8=S^3=5^3 = 125$ $cm^3$.
Surface - area $SA_8 = 6S^2=6\times5^2=6\times25 = 150$ $cm^2$.
| Shape | Dimensions | Volume | Surface Area |
|---|---|---|---|
| Rectangular Prism | $L = 9$cm, $W = 3$cm, $H = 2$cm | $54$ $cm^3$ | $102$ $cm^2$ |
| Rectangular Prism | $L = 12$m, $W = 4$m, $H = 4$m | $192$ $m^3$ | $224$ $m^2$ |
| Rectangular Prism | $L = 110$mm, $W = 20$mm, $H = 70$mm | $154000$ $mm^3$ | $22600$ $mm^2$ |
| Cube | $S = 6$cm | $216$ $cm^3$ | $216$ $cm^2$ |
| Cube | $S = 30$mm | $27000$ $mm^3$ | $5400$ $mm^2$ |
| Cube | $S = 8$m | $512$ $m^3$ | $384$ $m^2$ |
| Cube | $S = 5$cm | $125$ $cm^3$ | $150$ $cm^2$ |