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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.
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Explanation:

Step1: Recall the volume formula for a sphere

The volume \( V \) of a sphere is given by the formula \( V = \frac{4}{3}\pi r^3 \), where \( r \) is the radius of the sphere. Here, the radius \( r = 6.9 \) dam.

Step2: Substitute the values into the formula

First, calculate \( r^3 \): \( r^3=(6.9)^3 = 6.9\times6.9\times6.9 = 328.509 \)

Then, substitute \( \pi\approx3.14 \), \( r^3 = 328.509 \) into the volume formula:
\( V=\frac{4}{3}\times3.14\times328.509 \)

Step3: Calculate the volume in \( \text{dam}^3 \)

First, calculate \( \frac{4}{3}\times3.14=\frac{12.56}{3}\approx4.1867 \)

Then, multiply by \( 328.509 \): \( 4.1867\times328.509\approx1375.4707 \) (rounded to 4 decimal places)

Step4: Convert \( \text{dam}^3 \) to \( \text{m}^3 \)

We know that \( 1 \) dam (decameter) \( = 10 \) m, so \( 1 \text{dam}^3=(10)^3 \text{m}^3 = 1000 \text{m}^3 \)

To convert the volume from \( \text{dam}^3 \) to \( \text{m}^3 \), multiply the volume in \( \text{dam}^3 \) by \( 1000 \):
\( 1375.4707\times1000 = 1375470.7 \) (rounded to 4 decimal places, it is \( 1375470.7000 \))

Answer:

Volume (in \( \text{dam}^3 \)): \( \boldsymbol{1375.4707} \)

Volume (in \( \text{m}^3 \)): \( \boldsymbol{1375470.7000} \)