Question

The surface area of the sphere is i) 156 cm^2. find its volume

Answer 1

`\displaystyle{52\sqrt{(39)/(\pi)} \ \: \text{cm}^3}`

Explanation:

The surface area of the sphere has formula of
`\displaystyle{4\pi r^2}` where r is radius. Therefore, set the equation:

`\displaystyle{4\pi r^2=156}`

Divide both sides by 156:

`\displaystyle{(4\pir^2)/(4)=(156)/(4)}\\\\\displaystyle{\pi r^2=39}`

Then divide both sides by
`\displaystyle{\pi}`:

`\displaystyle{(\pi r^2)/(\pi) = (39)/(\pi)}\\\\\displaystyle{r^2=(39)/(\pi)`

Square root both sides:

`\displaystyle{√(r^2)=\sqrt{(39)/(\pi)}}\\\\\displaystyle{r=\pm\sqrt{(39)/(\pi)}}`

However, radius can only be positive. Therefore:

`\displaystyle{r=\sqrt{(39)/(\pi)}}`

To find the volume, we have to know that the sphere's volume is:

`\displaystyle{(4)/(3)\pi r^3}`

Thus, substitute the value of r in:

`\displaystyle{\text{V} = (4)/(3)\pi \cdot \left(\sqrt{(39)/(\pi)}\right)^3}\\\\\displaystyle{\text{V} = (4)/(3)\pi \cdot (39)/(\pi)\sqrt{(39)/(\pi)}}\\\\\displaystyle{\text{V} = 52 \sqrt { (39)/(\pi)}}`

Therefore, the volume of sphere is:

`\displaystyle{52\sqrt{(39)/(\pi)} \ \: \text{cm}^3}`