#How do I do this?
lucid bramble
i used Volume = Volume relationship to get the height from P to triangle ABC which is 2sqrt(6)/3. i am pretty sure that PB is just the height so i just used pythagorean theorem to get the diameter and then the radius which is sqrt(33)/12. and then i found the surface area which is 11pi/12 but it says it is wrong
foggy violet
My image is not the best, but I think it is good enough. If $h$ is the height of the pyramid, we have $\dfrac{\sqrt{2}}{6}=V=\dfrac{1}{3}S\cdot h=\dfrac{1}{3}\cdot\dfrac{\sqrt{3}}{4} h$, we find $h=\dfrac{2\sqrt{6}}{3}$. By similarity of triangles, from $H$ to the center of the equilateral triangle will be half of this $h$, namely, $\dfrac{\sqrt{6}}{3}$. If $R$ is the radius of the sphere, then using Pythagoras Theorem, $R^2=\Big(\dfrac{\sqrt{6}}{3}\Big)^2+\Big(\dfrac{\sqrt{3}}{3}\Big)^2=1$. Hence, the surface area of the sphere is $4\pi$. Do you know the correct answer?
amber sageBOT
Babak
