Given:
Base area of the cuboid = 180 cm²
Volume of the cuboid = 900 cm³

To find:
Height of the cuboid

Solution:

To find the height of the cuboid, we can use the formula:

Volume = Base area × Height

Step 1: Finding the base length and base width
Since the base area is given as 180 cm², we need to find the dimensions of the base.

Let's assume the base length to be 'l' and the base width to be 'w'.

Therefore, the base area can be calculated as:

Base area = length × width
180 cm² = l × w

Step 2: Finding the base length and base width factors
To find the factors of 180, we can list all the possible pairs of numbers that multiply to give the product 180.

Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

Step 3: Determining the base length and base width
We need to find the pair of factors that can be multiplied to give the base area of 180 cm².

From the factors of 180, we can see that the pair of factors that multiply to give 180 are 10 and 18.

Therefore, the base length (l) = 18 cm and the base width (w) = 10 cm.

Step 4: Finding the height of the cuboid
Now that we know the base length and base width, we can substitute them into the formula to find the height.

Volume = Base area × Height
900 cm³ = 180 cm² × Height

Dividing both sides of the equation by 180 cm², we get:

Height = 900 cm³ / 180 cm²
Height = 5 cm

Answer:
The height of the cuboid is 5 cm.