Question

A sphere and a right cylinder have equal volumes. The radius of the sphere = the radius of the cylinder. Compare the surface area of the sphere to the total area of the cylinder.

Answer 1

2:3

Answer 2

That is also what I got; but my answer key says "6:7" and I have no idea why.

Answer 3

ops 2:3 is the ratio of the volumes if r is constant,
the question is asking for the ratio of surface areas

Answer 4

Volume of Sphere = Volume of Right Circular Cylinder
4/3* π r ³ = π r ² h
4r/3 * π r ² = π r ² * h
4r/3 = h
4r = 3h
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Ratio of Surface Area of Sphere to Surface Area of Right Circular Cylinder

4π r ² / (2 π r h + 2π r²)
2r * 2 π r / 2 π r * (h + r)
2r / (h + r)
3/3 * 2r / (h + r)
6r / 3 (h + r)
6r / (3h + 3r)
Recall that 4r = 3h or 3h = 4r
6r / (4r + 3r)
6r / 7r
6/7 --> Ratio of Surface Areas of Sphere and Right Circular Cylinder with Equal Volumes

Answer 5

Unklerhaukus: I found the ratio of the volumes too, haha. Thanks though! Directix: that helped a ton :)