1 Answer

CaKa · Answer 1 · 2023-07-20T17:17:03+0000

You can identify that the whole solid is formed by a cylinder and a hemisphere.

The formula to calculate the volume of a cylinder is:

$V_c=\pi r^2h$

Where "r" is the radius and "h" is the height of the cylinder.

The formula to calculate the volume of a hemisphere is:

$V_h=(2)/(3)\pi r^3$

Where "r" is the radius.

Knowing these formulas, you can set up the following equation to calculate the total volume of the solid. Remember to use:

$\pi\approx3.14$

Then:

$V_t=(3.14\cdot r^2\cdot h)+((2)/(3)\cdot3.14\cdot r^3)$

You know that:

$\begin{gathered} r=8ft \\ h=9ft \end{gathered}$

Therefore, you can substitute values into the equation and evaluate:

$\begin{gathered} V_t=(3.14)(8ft)^2(9ft)+((2)/(3))(3.14)(8ft)^3 \\ \\ V_t=1808.64ft^3+1071.78667ft^3 \end{gathered}$
$V_t\approx2880.427ft^3$

Therefore, the answer is:

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