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Home » The volume of a hemisphere is half the volume of a sphere of the same radius. - SUpost

The volume of a hemisphere is half the volume of a sphere of the same radius. - SUpost

📅 July 7, 2026 👤 scraface

Jul 07, 2026

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Solution: First, compute the area using Heronâs formula. Let $ a = 7...
s = rac{7 + 10 + 13}{2} = 15
The area $ A $ is:
A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{15(15 - 7)(15 - 10)(15 - 13)...
\sqrt{1200} = \sqrt{100 \cdot 12} = 10\sqrt{12} = 10 \cdot 2\sqrt{3} =...
The altitude $ h $ corresponding to a side $ b $ is given by:
A = rac{1}{2} b h \Rightarrow h = rac{2A}{b}
To find the longest altitude, we use the shortest side, since altitude...
h_{ ext{longest}} = rac{2 \cdot 20\sqrt{3}}{7} = rac{40\sqrt{3}}{7}...
Thus, the length of the longest altitude is $ oxed{rac{40\sqrt{3}}{7...

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