Question

I am going to take a picture of the question as you can see the question has already been answered my teacher wants me to show how she got the answer.

Answer 1

The surface area of a sphere is given by the equation;

`4\pi r^2`

The ratio of the surface areas of the two spheres can be expressed as;

`\begin{gathered} 4\pi r^2_1\colon4\pi r^2_2\text{ = 1:16} \\ \text{The equation becomes:} \\ \\ r^{2\text{ }}_1\colon r^2_2\text{ = 1:16 (The 4}\pi s\text{ cancel out each other)} \\ \text{The equation above implies;} \\ r^2_1\text{ = 1 }\Rightarrow r_1=1 \\ r^2_2\text{ = 16 }\Rightarrow r_2\text{ = 4} \end{gathered}`

The volume of a sphere is given by the equation:

`V\text{ = }(4)/(3)\pi r^3^{}`
`\begin{gathered} \text{For r}_1\text{ = 1} \\ V_1=\text{ }(4)/(3)\text{ x }\pi x1^{3\text{ }}\text{ }\Rightarrow\text{ }(4)/(3)\pi \\ \\ \text{For r}_2\text{ = 4} \\ V_2=(4)/(3)_{}\text{ x }\pi x4^3 \\ \\ V_1\colon V_2\text{ = }(4)/(3)\pi\text{ : }(4)/(3)\pi x4^3 \\ ((4)/(3)\pi\text{ will cancel out each other)} \\ \\ We\text{ will be left with the equation:} \\ V_1\colon V_2=1\colon4^3\text{ }\Rightarrow\text{ 1:64} \end{gathered}`