Question

Volume of two spheres is in the ratio 64 : 125.Find the ratio of their surface areas.

Answer 1

VOLUME: Space occupied by an object is called a volume of that particular object. Volume is always measured in cube unit.

SURFACE AREA: Surface area of a solid body is the area of all of it surfaces together and it is always measured in square unit.

SPHERE:
A sphere is a solid generated by the revolution of a semicircle about its diameter.
Volume of sphere: (4/3)πr³
Surface area of sphere: 4πr²

SOLUTION:

Let the Radii be R1 & R2 & Surface areas are S1 & S2 of the two spheres & volume of Sphere with radius R1 is V1 and volume of Sphere with radius R2 is V2.

Given:
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.

HOPE THIS WILL HELP YOU...

Answer 2

Answer:

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