Question

Suppose the sphere below with radius rhas a surface area equal to 45 units?Find the surface area of the sphere with twice the radius.21A. 180 units2B. 180 units3C. 90 units2D. 90 units 3

Answer 1

It is given that the small sphere with radius r has a surface area equal to 45 units square.

The surface area of a sphere with radius r is given by;

`SA=4\pi r^2`

Since the surface area of the small sphere is 45 units square.

`\begin{gathered} \Rightarrow45=4\pi r^2 \\ \\ \Rightarrow(45)/(4\pi)=r^2 \\ \\ \Rightarrow r=\sqrt{(45)/(4\pi)} \end{gathered}`

To find the Surface area with twice the radius, we need to multiply the value of r by 2;

`\Rightarrow R=2r=2\sqrt{(45)/(4\pi)}`

Therefore, the surface area is of a sphere with a radius R is

`\begin{gathered} SA=4\pi R^2 \\ \\ \Rightarrow SA=4\pi(2\sqrt{(45)/(4\pi)})^2=4\pi(4*(45)/(4\pi))=4*45=180\text{ unit}^2 \end{gathered}`

Hence, the correct option is A.