UPSKILL MATH PLUS

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A solid sphere and a solid hemisphere have equal total surface area. Prove that the ratio of their volume is 3 \sqrt{3}:4.
 
Proof:
 
Let r_1 be the radius of a sphere and r_2 be the radius of a hemisphere.
 
πr12πr22=ii
 
r1r2=ii
 
Ratio of their volumes = iiπr1iiiπr2i
 
= ir1ir2i
 
= i×iiii
 
= iii
 
Hence, proved.