The volume of two spheres are in the ratio 125 is to 27 find the ratio of their surface area

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Volume of two hemispheres are in the ratio 27: 125. Find the ratio of their radii.

Volume of two spheres in the ratio 64:125 find the ratio of there surface areas

Posted by Manish Pal 2 years, 3 months ago

Ratio of volumes of two spheres = V1/V2 = 64 /125

Volume of sphere = (4/3)πr³
V1/V2 = 64/125
(4/3)πR1³ / (4/3)πR2³ = 64/125
R1³ / R2³ = 64/125
(R1/R2)³ = 64/125
(R1/R2)= ³√64/125

R1/R2 = ⅘

Surface area of sphere: 4πr²
S1/S2 = 4πR1² / 4πR2²
S1/S2= R1² / R2²
S1/S2 = (R1/R2)²
S1/S2 = (⅘)²
S1/S2 = 16/25
S1 : S2 = 16 : 25
Hence, the ratio of their Surface areas = 16 : 25.

16:25

16:25