1 Answer

Adam Plocher · Answer 1 · 2023-10-26T01:07:38+0000

The rule of the volume of the hemisphere is

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

r is the radius of it

Since the diameter of the hemisphere is double the radius, then we can find the radius then multiply it by 2 to find it

Since the volume of the hemisphere is 841 cm^3, then

Substitute V by 841

$\begin{gathered} 841=(2)/(3)\pi(r^3) \\ 841=(2)/(3)\pi r^3 \end{gathered}$

Divide both sides by 2/3pi

$\begin{gathered} (841)/((2)/(3)\pi)=((2)/(3)\pi r^3)/((2)/(3)\pi) \\ \\ (2523)/(2\pi)=r^3 \end{gathered}$

Take cube root to both sides

$\begin{gathered} \sqrt[3]{(2523)/(2\pi)}=\sqrt[3]{r^3} \\ 7.377555082=r \end{gathered}$

Multiply it by 2 to find the diameter, then round it to the nearest tenth

$\begin{gathered} d=7.377555082*2 \\ d=14.75511016 \\ d=14.8\text{ cm} \end{gathered}$

The diameter of the hemisphere is 14.8 cm

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