https://file.aiquickdraw.com/mathbot/file/1727189197561rwc1tf6y.jpg

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.

Calculate the volume of the frustum. If your answer is a decimal, give it to 1 d.p.

Learn how to calculate the volume of a frustum using the given height and areas of the top and base. This problem involves applying the formula for the volume of a frustum of a pyramid or cone with specific measurements: height = 54 cm, top area = 10 cm², base area = 90 cm². Suitable for high school students in Grades 9-12.

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