Homework Help: solid mensuration

Posted by ylzik on Tuesday, March 10, 2009 at 10:16am.

is what i've been doing correct so far:

find the value of h for a spherical segment whose volume is equivalent to 159pi if the radii of the bases are 5m and 4m respectively

v= (pi/6)(3a^2 + 3b^2 + h^2) h

v= 0.52 ((3)(5^2) + (3)(4^2) + h^2) h

= 0.52 ((3)(25) + (3)(16) + h^2) h

= 0.52 (75 + 48 + h^2) h

=(39 + 24.96 + 0.52h^2) h

=(63.96 + 0.52h^2) h

if so, how do i find the value of h?

if not, where did i go wrong?

thank youuuuu so much for any help!!!

solid mensuration - Reiny, Tuesday, March 10, 2009 at 5:18pm
looks like you are using
V = (Pi/6)(3r1^2+3r2^2+h^2)h

where r1 and r2 are the two radii

but you are given that the volume is 159pi

159pi = pi/6(75 + 48 + h^2)h
954 = 123h + h^3
h^3 + 123h - 954 = 0

this solves for h = 6 and 2 complex roots.

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