Question

a cuboid has a length of (4x + 5\text{ cm}), a width of (x + 3\text{ cm}) and a height of (3x\text{ cm}).
its length is (10\text{ cm}) longer than its height.

calculate the volume of the cuboid.

Explanation:

⚡ Using what you learned: calculating volume of rectangular prisms

Step 1: Set up the equation for \( x \)

The problem states that the length is \( 10\text{ cm} \) longer than the height:

$$ \text{Length} = \text{Height} + 10 $$

Substitute the given expressions:

$$ 4x + 5 = 3x + 10 $$

Solve for \( x \):

$$ 4x - 3x = 10 - 5 $$

$$ x = 5 $$

Step 2: Calculate the dimensions of the cuboid

Substitute \( x = 5 \) into the expressions for length, width, and height:

$$ \text{Length} = 4(5) + 5 = 25\text{ cm} $$

$$ \text{Width} = 5 + 3 = 8\text{ cm} $$

$$ \text{Height} = 3(5) = 15\text{ cm} $$

Step 3: Calculate the volume

The volume \( V \) of a cuboid (rectangular prism) is:

$$ V = \text{Length} \times \text{Width} \times \text{Height} $$

$$ V = 25 \times 8 \times 15 $$

$$ V = 200 \times 15 = 3000\text{ cm}^3 $$

Answer:

\( 3000\text{ cm}^3 \)