Sphere and cone

Within the sphere of radius G = 33 cm inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone?

Correct answer:

r =  31.11 cm
h =  44 cm
V =  44602.24 cm3

Step-by-step explanation:

G=33 cm V=31πr2h h=G+x=33+x G2=x2+r2 r2=G2x2 V=31π(G2x2)(G+x) V=31π(G3+G2xGx2x3)  V=31π(G22Gx3x2) V=0 G22Gx3x2=0 3x266x+1089=0 3x2+66x1089=0  a=3;b=66;c=1089 D=b24ac=66243(1089)=17424 D>0  x1,2=2ab±D=666±17424 x1,2=666±132 x1,2=11±22 x1=11 x2=33   Factored form of the equation:  3(x11)(x+33)=0   h=G+x1=33+11=44 cm r=G2x12=31.11 cm 
h=33+11=44 cm
V=31πr2h=44602.24 cm3

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Showing 1 comment:
Dr Math
that's very mind blowing

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