Question

volume of pyramids maze
shade the arrow with the correct answer to complete the maze.

some of the dimensions of a triangular pyramid are shown in the diagram. the volume of the pyramid is 864 cubic meters.
what is the height of the triangular pyramid in meters?

a handmade chocolate treat in the shape of a rectangular pyramid has a height of 10 centimeters. the area of the base of the chocolate treat is 45 square centimeters.
what is the volume of the handmade chocolate treat in cubic centimeters?

the dimensions of a square pyramid are shown in the diagram.
a puzzle is in the shape of a triangular

Explanation:

Step1: Recall pyramid volume formula

The volume of any pyramid is given by $V = \frac{1}{3} \times B \times h$, where $B$ is the area of the base, and $h$ is the height of the pyramid.

---

First problem (triangular pyramid height):

Step1: Calculate base area

The base is a triangle with base $18$ m and height $24$ m.
$B = \frac{1}{2} \times 18 \times 24 = 216$ $\text{m}^2$

Step2: Solve for height $h$

We know $V=864$ $\text{m}^3$. Rearrange the volume formula:
$h = \frac{3V}{B}$
$h = \frac{3 \times 864}{216} = 12$ $\text{m}$

---

Second problem (chocolate treat volume):

Step1: Plug values into volume formula

We know $B=45$ $\text{cm}^2$, $h=10$ $\text{cm}$.
$V = \frac{1}{3} \times 45 \times 10$

Step2: Compute the volume

$V = 15 \times 10 = 150$ $\text{cm}^3$

Answer:

Height of the triangular pyramid: $\boldsymbol{12}$ meters
Volume of the chocolate treat: $\boldsymbol{150}$ cubic centimeters