V_2 = \frac{4}{3} \pi (3r)^3 = \frac{4}{3} \pi \cdot 27r^3 = 27 \cdot \frac{4}{3} \pi r^3 = 27V_1
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- Let the original radius be \(r\), so original volume is:
- V_1 = \frac{4}{3} \pi r^3
- After tripling the radius, new radius is \(3r\), so new volume \(V_2\) is:
- Thus, the volume increases by a factor of \(\boxed{27}\).
- Question:** In a right triangle, one leg is 6 cm and the hypotenuse is 10 cm. Find the length of the shortest altitude.
- Let the triangle have legs \(a = 6\) cm, hypotenuse \(c = 10\) cm. Use the Pythagorean theorem to find the other leg \(b\):
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