Math Snap

STEP 1

What is this asking?
We need to find the volume of a pyramid with a square base, given the side length of the base and the pyramid's height.
Watch out!
Don't mix up the formulas for the volume of a pyramid and the volume of a prism!

STEP 2

1. Find the area of the square base.
2. Calculate the pyramid's volume.
3. Round to the nearest tenth.

STEP 3

Alright, let's start by finding the area of the square base.
We know the side length is $4.6$ m.
The area of a square is side length times side length, right?

STEP 4

So, the area of the base is $4.6 \text{ m} \cdot 4.6 \text{ m} = 21.16 \text{ m}^2$.
Boom!

STEP 5

Now, the volume of a pyramid is $\frac{1}{3}$ times the area of the base times the height.
We just found the area of the base, which is $21.16 \text{ m}^2$, and we know the height of the pyramid is $7.2$ m.

STEP 6

Let's plug those values into our formula:
$$\text{Volume} = \frac{1}{3} \cdot 21.16 \text{ m}^2 \cdot 7.2 \text{ m}$$

STEP 7

Multiplying those together, we get:
$$\text{Volume} = \frac{1}{3} \cdot 152.352 \text{ m}^3$$

STEP 8

Dividing by three gives us the volume:
$$\text{Volume} = 50.784 \text{ m}^3$$

STEP 9

We're almost there!
We need to round our answer to the nearest tenth.
Our calculated volume is $50.784 \text{ m}^3$.
The digit in the hundredths place is $8$, which is greater than or equal to $5$, so we round up.

STEP 10

Therefore, the rounded volume is $50.8 \text{ m}^3$.
Fantastic!

The volume of the pyramid is approximately $50.8 \text{ m}^3$.