Question

the shape below is formed of a cuboid with a smaller cuboid removed from its corner.

work out the volume of the shape.

not drawn accurately

Explanation:

⚡ Using what you learned: Volume of Composite Solids

Step 1: Volume of the large cuboid

Calculate the volume of the entire cuboid before the corner was removed:

$$ V_{\text{large}} = 18 \times 13 \times 24 $$

$$ V_{\text{large}} = 5616 \text{ cm}^3 $$

Step 2: Dimensions of the removed cuboid

Identify the dimensions of the smaller cuboid that was removed from the corner:

• Height: \( 2 \text{ cm} \)
• Depth: \( 13 \text{ cm} \) (the depth is constant throughout the shape)
• Width: \( 18 - 12 = 6 \text{ cm} \)

Step 3: Volume of the removed cuboid

Calculate the volume of this smaller corner cuboid:

$$ V_{\text{removed}} = 6 \times 13 \times 2 $$

$$ V_{\text{removed}} = 156 \text{ cm}^3 $$

Step 4: Total volume of the shape

Subtract the removed volume from the large cuboid's volume:

$$ V_{\text{total}} = 5616 - 156 $$

$$ V_{\text{total}} = 5460 \text{ cm}^3 $$

Answer:

\( 5460 \text{ cm}^3 \)