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An illustration showing two cubes joined on both sides of a cuboid. The sides of the cube are 5 centimeters. The length of the cuboid is 10 centimeters and height is 12 centimeters.

What is the volume of the composite figure?

(1 point)
Responses

850 cm3
850 cm cubed

170 cm3
170 cm cubed

370 cm3
370 cm cubed

725 cm3
725 cm cubed
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1 answer

To find the volume of the composite figure, we will calculate the volumes of both the cubes and the cuboid separately and then add them together.

  1. Volume of the cubes: Each cube has a side length of 5 cm. The volume \( V \) of a cube is given by the formula: \[ V = s^3 \] where \( s \) is the side length. So for one cube: \[ V = 5^3 = 125 , \text{cm}^3 \] Since there are two cubes: \[ V_{\text{cubes}} = 2 \times 125 = 250 , \text{cm}^3 \]

  2. Volume of the cuboid: The cuboid has a length of 10 cm, width of 5 cm (equal to the side of the cubes), and height of 12 cm. The volume \( V \) of a cuboid is given by the formula: \[ V = l \times w \times h \] Substituting the values: \[ V = 10 , \text{cm} \times 5 , \text{cm} \times 12 , \text{cm} = 600 , \text{cm}^3 \]

  3. Total volume of the composite figure: We now combine the volume of the cubes and the cuboid: \[ V_{\text{total}} = V_{\text{cubes}} + V_{\text{cuboid}} = 250 , \text{cm}^3 + 600 , \text{cm}^3 = 850 , \text{cm}^3 \]

Thus, the volume of the composite figure is \( \boxed{850 , \text{cm}^3} \).