The cross section of a prism is a triangle ABC with angle ABC = 90°, AB = 10cm and BC = 6cm. If the prism is 30cm high, what is its volume?
Understand the Problem
The question asks to calculate the volume of a prism given its cross-section is a right-angled triangle with sides AB = 10 cm and BC = 6 cm, and the prism's height is 30 cm. We need to use the formula: Volume = (Area of the base) * height
Answer
The volume of the prism is $900 \text{ cm}^3$.
Answer for screen readers
The volume of the prism is $900 \text{ cm}^3$.
Steps to Solve
- Calculate the area of the right-angled triangle
The area of a triangle is given by the formula: Area = $\frac{1}{2} \times base \times height$. Since angle ABC = 90°, we can use AB and BC as the base and height of the triangle. Area = $\frac{1}{2} \times 10 \times 6 = 30 \text{ cm}^2$
- Calculate the volume of the prism
The volume of a prism is given by the formula: Volume = (Area of the base) $\times$ height. In this case, the base is the right-angled triangle, and the height of the prism is given as 30 cm.
Volume = $30 \text{ cm}^2 \times 30 \text{ cm} = 900 \text{ cm}^3$
The volume of the prism is $900 \text{ cm}^3$.
More Information
The volume is measured in cubic centimeters because we are multiplying area (which is in square centimeters) by height (which is in centimeters).
Tips
A common mistake would be to forget the $\frac{1}{2}$ factor when calculating the area of the triangle, or to confuse the height of the triangle with the height of the prism.
AI-generated content may contain errors. Please verify critical information
