Question

find the volume of the solid shown above. (the solid is not drawn to scale and remember to use \\( \pi \approx 3.14 \\) for all calculations involving \\( \pi \\)).
volume = \\( \boxed{\quad} \\) dam³
round answers to 4 decimal place as needed.
volume = \\( \boxed{\quad} \\) m³
round answers to 4 decimal place as needed.
question help: message instructor

Explanation:

Step1: Find the radius of the sphere

The diameter of the sphere is given as \( 6.9 \, \text{dam} \). The radius \( r \) is half of the diameter, so \( r=\frac{6.9}{2}=3.45 \, \text{dam} \).

Step2: Use the formula for the volume of a sphere

The formula for the volume \( V \) of a sphere is \( V = \frac{4}{3}\pi r^{3} \). We are given \( \pi\approx3.14 \) and \( r = 3.45 \, \text{dam} \). Substitute these values into the formula:
\[

$$\begin{align*} V&=\frac{4}{3}\times3.14\times(3.45)^{3}\\ &=\frac{4}{3}\times3.14\times3.45\times3.45\times3.45\\ &=\frac{4}{3}\times3.14\times40.995375\\ &=\frac{4\times3.14\times40.995375}{3}\\ &=\frac{515.50635}{3}\\ & = 171.83545 \, \text{dam}^3 \end{align*}$$

\]

Step3: Convert the volume from \( \text{dam}^3 \) to \( \text{m}^3 \)

We know that \( 1 \, \text{dam}=10 \, \text{m} \), so \( 1 \, \text{dam}^3=(10)^{3}\text{m}^3 = 1000 \, \text{m}^3 \). To convert \( 171.83545 \, \text{dam}^3 \) to \( \text{m}^3 \), we multiply by \( 1000 \):
\( 171.83545\times1000 = 171835.45 \, \text{m}^3 \)

Answer:

Volume in \( \text{dam}^3 \): \( 171.8355 \) (rounded to 4 decimal places)
Volume in \( \text{m}^3 \): \( 171835.4500 \) (rounded to 4 decimal places)