A sphere is melted and molded into solid cylinder. If radius of both solids is…
2020
A sphere is melted and molded into solid cylinder. If radius of both solids is equal, then find the ratio of total surface area of sphere to the total surface area of cylinder
Answer: D. 6 : 7 — Let the common radius be r. Sphere volume = 4/3*pi*r^3. Cylinder volume = pi*r^2*h. Equating volumes gives h = 4r/3. Cylinder TSA = 2*pi*r*(r+h) =…
- A.
2 : 3
- B.
4 : 3
- C.
3 : 7
- D.
6 : 7
- E.
7 : 6
Show answer & explanation
Correct answer: D
Let the common radius be r. Sphere volume = 4/3*pi*r^3. Cylinder volume = pi*r^2*h. Equating volumes gives h = 4r/3. Cylinder TSA = 2*pi*r*(r+h) = 2*pi*r*(r+4r/3) = 14/3*pi*r^2. Sphere TSA = 4*pi*r^2. Ratio = 4 : 14/3 = 6 : 7.
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