To double the volume, we have to increase the radius by multiplying it by <span>3<span>√2</span></span>.
let <span><span>R1</span>=R<span>3<span>√2</span></span></span> Then the volume of a sphere with radius <span>R1</span> will be <span><span>V1</span>=<span>43</span>π<span>R<span>31</span></span>=<span>43</span>π<span><span>(R<span>3<span>√2</span></span>)</span>3</span>=<span>83</span>π<span>R3</span></span> - twice larger than original volume.
With radius <span><span>R1</span>=R<span>3<span>√2</span></span></span> the surface area of a new sphere will be <span>4π<span>R<span>21</span></span>=4π<span>R2</span><span><span>(<span>3<span>√2</span></span>)</span>2</span>=4<span>3<span>√4</span></span>π<span>R2</span></span>
The ratio of the new surface area to the old one equals to <span><span><span>4<span>3<span>√4</span></span>π<span>R2</span></span><span>4π<span>R2</span></span></span>=<span>3<span>√<span>4</span></span></span></span>
The easiest method is to find the x-intercepts of the quadratic function by substituting y=0 in the function and solving it to find the possible values of x. The number of all possible values of x is the number of x-intercepts of the graph.
The graph of a linear function is a straight line, but a vertical line is not the graph of a function. All linear functions are written as equations and are characterized by their slope and y -intercept.