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

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

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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where $A$ is the area of the triangle and $s$ is the semi-perimeter:
s = \frac{a + b + c}{2} = \frac{13 + 14 + 15}{2} = 21
Using Heron’s formula for area:
r = \frac{84}{21} = 4
$$Question: What is the largest possible value of $\gcd(a,b)$, if the...
Let $d = \gcd(a,b)$. Then we can write $a = dx$, $b = dy$, where $\gcd...
dx + dy = d(x + y) = 1000 \Rightarrow d \mid 1000
So $d$ must be a divisor of 1000. Also, both $a$ and $b$ must be divis...
To maximize $d$, we look at the largest divisor of 1000 such that $x =...
The prime factorization of 1000 is:

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