Question

The surface area of a sphere is 2464 cm². If its radius be doubled, then what will be the surface area of the new sphere?

Answer 1

Let the radii of the given sphere and the new sphere be r and R, respectively. 

We have,

R = 2r and the surface area of the given sphere = 24 cm²

`i.e. 4pir^2 = 2464  cm<sup>2</sup>`

The surface area of the given sphere = 2464 cm²                     

${\displaystyle i.e4\pi r^2=2426}$ cm²  

The surface area of the new sphere = 4πR²

${\displaystyle =4\pi {\left(2r\right)}^2}$ 

${\displaystyle =4\pi {\left(4r\right)}^2}$ 

${\displaystyle =4\left(4\pi r^2\right)}$

${\displaystyle =4\times 2464}$

${\displaystyle =9856 c{m}^2}$

So, the surface area of the new sphere is 9856 cm².