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To find the volume of the shape first we have to split the shape into two rectangles; a large one at the bottom and a small one at the top. The formula to find volume of a rectangle is

[tex]v = length \times width \times height[/tex]

note that after both volumes are found they should be added to determine the volume of the entire shape*

The length of the large rectangle is 5m, the width is 7m, and the height is 6m. Therefore the volume is

[tex]v = l \times w \times h \\ v = 5 \times 7 \times 6 \\ v = 210 {m}^{3} [/tex]

The length of the small rectangle is 5m, the width is 3m, and the height is 1m. Therefore the volume is

[tex]v = l \times w \times h \\ v = 5 \times 3 \times 1 \\ v = 15 {m}^{3} [/tex]

[tex]210 {m}^{3} + 15 {m}^{3} = 225 {m}^{3} \\ therefore \: the \: volume \: of \: the \: \\ entire \: shape \: is: \\ 225 {m}^{3} [/tex]

igoroleshko156 igoroleshko156 · Answer 2 · 2022-05-12T06:29:56+02:00

Answer:

[tex]V_{\ total}=225\ m^3[/tex]

Step-by-step explanation:

Step 1: Find the volume of the big box

[tex]V_{\ big} = l * w * h[/tex]

[tex]V_{\ big} = 7\ m * 5\ m * 6\ m[/tex]

[tex]V_{\ big} = 210\ m^3[/tex]

Step 2: Find the volume of the small box

[tex]V_{\ small} = l * w * h[/tex]

[tex]V_{\ small} = 3\ m * 5\ m * (7\ m - 6\ m)[/tex]

[tex]V_{\ small} = 3\ m * 5\ m * 1\ m[/tex]

[tex]V_{\ small} = 15\ m^3[/tex]

Step 3: Combine the volumes

[tex]V_{\ total}=V_{\ big} + V_{\ small}[/tex]

[tex]V_{\ total}=210\ m^3 + 15\ m^3[/tex]

[tex]V_{\ total}=225\ m^3[/tex]

Answer: [tex]V_{\ total}=225\ m^3[/tex]