The image shows a frustum with the following details:

• Height of the frustum, $h = 54$ cm.
• Area of the top of the frustum, $A_1 = 10$ cm².
• Area of the base of the frustum, $A_2 = 90$ cm².

To calculate the volume of the frustum, we use the formula for the volume of a frustum of a pyramid or cone:

$V = \frac{h}{3} \times \left( A_1 + A_2 + \sqrt{A_1 \times A_2} \right)$

Where:

• $V$ is the volume of the frustum.
• $h$ is the height.
• $A_1$ and $A_2$ are the areas of the top and base, respectively.

Let's calculate the volume using this formula.The volume of the frustum is $2340.0 \, \text{cm}^3$.

Would you like any further details or have any questions?

Here are 5 related questions to explore:

1. How do you calculate the volume of a cone if the frustum had no top?
2. What is the difference between a frustum of a pyramid and a frustum of a cone?
3. How does the formula for the volume of a frustum change if the shape is a cylinder?
4. Can the surface area of this frustum be calculated, and how?
5. What happens to the volume if the height of the frustum is doubled?

Tip: Always check if the areas provided are for the faces parallel to the base and top when using this formula.