Question
The tap on candy comes in a package like that the triangular prism the bases of the triangle 2 inches with the height of 2.5 inches. The faces are 10 inches in length. What is the volume of the package?
Answers
GPT-4o mini
To find the volume of a triangular prism, you can use the formula:
\[
\text{Volume} = \text{Base Area} \times \text{Height of the Prism}
\]
1. **Calculate the area of the triangular base**. The base is a triangle with a base length \( b = 2 \) inches and a height \( h = 2.5 \) inches. The area of a triangle is given by:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \times 2.5 = \frac{1}{2} \times 5 = 2.5 \text{ square inches}
\]
2. **Dimensions of the prism**: The height of the prism is the length of the triangular prism, which is given as \( h = 10 \) inches.
3. **Calculate the volume**:
\[
\text{Volume} = \text{Base Area} \times \text{Height of the Prism} = 2.5 \times 10 = 25 \text{ cubic inches}
\]
So, the volume of the package is **25 cubic inches**.
\[
\text{Volume} = \text{Base Area} \times \text{Height of the Prism}
\]
1. **Calculate the area of the triangular base**. The base is a triangle with a base length \( b = 2 \) inches and a height \( h = 2.5 \) inches. The area of a triangle is given by:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \times 2.5 = \frac{1}{2} \times 5 = 2.5 \text{ square inches}
\]
2. **Dimensions of the prism**: The height of the prism is the length of the triangular prism, which is given as \( h = 10 \) inches.
3. **Calculate the volume**:
\[
\text{Volume} = \text{Base Area} \times \text{Height of the Prism} = 2.5 \times 10 = 25 \text{ cubic inches}
\]
So, the volume of the package is **25 cubic inches**.