Question

the prism below has a front face formed from a rectangle with a rectangular hole.

work out the volume of the prism.
give your answer in \\(\text{cm}^3\\).

Explanation:

⚡ Using what you learned: Volume of Composite Solids · Unit Conversion (metric and customary)

Step 1: Convert hole dimensions to cm

$$ \text{Width of hole} = 4\text{ mm} = \frac{4}{10}\text{ cm} = 0.4\text{ cm} $$

$$ \text{Height of hole} = 2\text{ mm} = \frac{2}{10}\text{ cm} = 0.2\text{ cm} $$

Step 2: Calculate the area of the front face

$$ \text{Area of large rectangle} = 6\text{ cm} \times 2\text{ cm} = 12\text{ cm}^2 $$

$$ \text{Area of rectangular hole} = 0.4\text{ cm} \times 0.2\text{ cm} = 0.08\text{ cm}^2 $$

$$ \text{Cross-sectional area} = 12\text{ cm}^2 - 0.08\text{ cm}^2 = 11.92\text{ cm}^2 $$

Step 3: Calculate the volume of the prism

$$ \text{Volume} = \text{Cross-sectional area} \times \text{length} $$

$$ \text{Volume} = 11.92\text{ cm}^2 \times 5\text{ cm} = 59.6\text{ cm}^3 $$

Answer:

59.6