Question

This triangular planting trough is 3.5 m long, 1.2 m wide at the top, and 0.75 m deep. How much soil will it hold?



(1 point)
Responses

4 cubic m
4 cubic m

3.15 cubic m
3.15 cubic m

1.575 cubic m
1.575 cubic m

0.5 cubic m

Answer 1

To calculate the volume of a triangular planting trough, you can use the formula for the volume \( V \) of a triangular prism:

\[
V = \text{Area of the base} \times \text{Height}
\]

1. **Calculate the area of the triangular base:**
The base of the trough is a triangle with a width (base) of 1.2 m and a height (depth) of 0.75 m. The area \( A \) of a triangle is given by:

\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

Plugging in the values:

\[
A = \frac{1}{2} \times 1.2 \, \text{m} \times 0.75 \, \text{m} = 0.45 \, \text{m}^2
\]

2. **Calculate the volume of the trough:**
Now, multiply the area by the length of the trough (3.5 m):

\[
V = A \times \text{length} = 0.45 \, \text{m}^2 \times 3.5 \, \text{m} = 1.575 \, \text{m}^3
\]

So, the triangular planting trough will hold **1.575 cubic meters** of soil.

The correct response is:

**1.575 cubic m**