Question

draw line(s) to show how you decomposed the figure. what is the volume of the figure? 4. 3 cm 4 cm 5 cm 2 cm 2×2×3 = 12 vb = 5×(2×2) = 20 v = 32 cm³ 5. 6 m 10 m 5 m 8 m 4 m v =

Explanation:

Step1: Decompose the first figure

Decompose the 3 - D figure into two rectangular prisms.

Step2: Calculate volume of first prism (top - left)

For the top - left prism with length $l = 3$ cm, width $w = 2$ cm and height $h = 2$ cm, the volume $V_1=l\times w\times h=3\times2\times2 = 12$ $cm^3$.

Step3: Calculate volume of second prism (bottom - right)

For the bottom - right prism with length $l = 5$ cm, width $w = 2$ cm and height $h = 2$ cm, the volume $V_2 = 5\times2\times2=20$ $cm^3$.

Step4: Calculate total volume of first figure

$V = V_1+V_2=12 + 20=32$ $cm^3$.

Step5: Decompose the second figure

Decompose the second 3 - D figure into two rectangular prisms. Let's assume we separate it into a large and a small prism. The large prism has length $l_1=8$ m, width $w_1 = 4$ m and height $h_1=10 - 5=5$ m. The small prism has length $l_2 = 6$ m, width $w_2 = 4$ m and height $h_2 = 5$ m.

Step6: Calculate volume of large prism of second figure

$V_{3}=l_1\times w_1\times h_1=8\times4\times5 = 160$ $m^3$.

Step7: Calculate volume of small prism of second figure

$V_{4}=l_2\times w_2\times h_2=6\times4\times5=120$ $m^3$.

Step8: Calculate total volume of second figure

$V'=V_{3}+V_{4}=160 + 120=280$ $m^3$.

Answer:

For the first figure: $32$ $cm^3$.
For the second figure: $280$ $m^3$.