Question

find the volume of this square based pyramid.
\\(v = ?\text{ cm}^3\\)
round to the nearest tenth.

Explanation:

Identify the given dimensions

We are given a square-based pyramid with:

• Base side length \(s = 5\text{ cm}\)
• Height of the pyramid \(h = 5\text{ cm}\)

Calculate the base area

Using the Volume of a Pyramid concept, we first find the area of the square base \(B\):

$$ B = s^2 = 5^2 = 25\text{ cm}^2 $$

Calculate the volume

Using the Volume of a Pyramid formula:

$$ V = \frac{1}{3} \cdot B \cdot h $$

Substitute the values:

$$ V = \frac{1}{3} \cdot 25 \cdot 5 = \frac{125}{3}\text{ cm}^3 $$

Round to the nearest tenth

Convert the fraction to a decimal:

$$ V \approx 41.6667\text{ cm}^3 $$

Rounding to the nearest tenth gives:

$$ V \approx 41.7\text{ cm}^3 $$

Answer:

Find the volume of this square based pyramid.

\(V =\) <blank>41.7</blank> \(\text{cm}^3\)

Round to the nearest tenth.