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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

170 cm3
170 cm cubed

725 cm3
725 cm cubed

850 cm3
850 cm cubed

370 cm3
370 cm cubed
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1 answer

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

  1. Volume of the Cuboid: The volume \( V \) of a cuboid is given by the formula: \[ V = \text{length} \times \text{width} \times \text{height} \] Here, the length is given as 10 cm, the width can be inferred to be equal to the side length of the cubes (5 cm), and the height is given as 12 cm.

    \[ V_{\text{cuboid}} = 10 , \text{cm} \times 5 , \text{cm} \times 12 , \text{cm} = 600 , \text{cm}^3 \]

  2. Volume of the Cubes: The volume \( V \) of a cube is given by: \[ V = \text{side}^3 \] The side length of each cube is 5 cm.

    \[ V_{\text{cube}} = 5 , \text{cm} \times 5 , \text{cm} \times 5 , \text{cm} = 125 , \text{cm}^3 \] Since there are 2 cubes, the total volume for both cubes is: \[ V_{\text{cubes}} = 2 \times 125 , \text{cm}^3 = 250 , \text{cm}^3 \]

  3. Total Volume of the Composite Figure: Now we add the volumes of the cuboid and the cubes together: \[ V_{\text{total}} = V_{\text{cuboid}} + V_{\text{cubes}} = 600 , \text{cm}^3 + 250 , \text{cm}^3 = 850 , \text{cm}^3 \]

Therefore, the volume of the composite figure is 850 cm³.