Question

consider the following figure.
complete the sentence describing the figure and its volume.
the figure is a triangular pyramid and has a volume of
cm³.
related content
volume of a pyramid or cone
article
volume of triangular prism & cube

Explanation:

Step1: Identify the base area

The base of the triangular pyramid is a right triangle with legs 5 cm and 3 cm. The area of a triangle is $\frac{1}{2} \times base \times height$. So, base area $B = \frac{1}{2} \times 5 \times 3 = 7.5$ $cm^2$.

Step2: Use the volume formula for a pyramid

The volume $V$ of a pyramid is given by $V = \frac{1}{3} \times B \times h$, where $h$ is the height of the pyramid. Here, the height $h = 10$ cm (from the figure). Substituting $B = 7.5$ and $h = 10$ into the formula: $V = \frac{1}{3} \times 7.5 \times 10$.

Step3: Calculate the volume

First, multiply 7.5 and 10: $7.5 \times 10 = 75$. Then, divide by 3: $\frac{75}{3} = 25$.

Answer:

25