Question

The volume of a sphere is 28/3 times it surface area, find the surface area​

Answer 1

The surface area of a sphere, given that its volume is 28/3 times its surface area, is found to be 196 π square units.

Step-by-step explanation:

The student is asking for the surface area of a sphere given that its volume is 28/3 times its surface area. We use the formulas for the volume and surface area of a sphere:

Volume of a sphere: V = 4/3 π r^3

Surface area of a sphere: A = 4 π r^2

According to the given information, V = (28/3)A. We can substitute the formulas for V and A into this equation to get:

(4/3 π r^3) = (28/3)(4 π r^2)

Cancelling out the common terms and solving for r gives us:

r = 7

Now, plug the value of r back into the formula for surface area:

A = 4 π r^2

A = 4 π (7)^2

A = 4 π 49

A = 196 π

So, the surface area of the sphere is 196 π square units.

Answer 2

615.44 units squared

Step-by-step explanation:

Let the volume and surface area of the sphere be V and S respectively.

`\therefore V = (28)/(3) * S\\\\\therefore (4)/(3) \pi {r}^(3) = (28)/(3) \pi {r}^(2) \\ \\ \frac{ {r}^(3) }{ {r}^(2) } = (28\pi)/(3) * (3)/(4\pi) \\ \\ r = 7 \: units \\ \\ \because S = 4\pi {r}^(2) \\ \\ \therefore \: S = 4 * 3.14 * {7}^(2) \\ \\ \therefore \: S = 12.56 * 49 \\ \\ \therefore \: S =615.44 \: {units}^(2)`