How much paint do you need?

let $A_S$ be the area of the sphere

by ratio and proportion, we get

$\dfrac{A_S}{6.28}=\dfrac{50}{1}$ $\implies$ $A_S=314~m^2$

the area of the sphere is given by the formula $A_S=4 \pi r^2$ , substituting, we get

$314=4(3.14)(r^2)$ $\implies$ $r^2=25$ $\implies$ $r=5$

the surface area of a cube is given by the formula $A_C=6a^2$ , but $a=r=5$ , substituting, we get

$A_C=6(5^2)=6(25)=150~m^2$

let $N$ be the number of quarts needed for the cube, then

$N=150~m^2\left(\dfrac{1~quart}{50~m^2}\right)=$ $\color{#D61F06}\large \boxed{3~quarts}$

The sphere's surface area, as implied by the given conditions, is $50 \times 6.28 = 314 m^{2}$ . According to the formula for the surface area of a sphere ( $SA=4πr^{2}$ ), it is clear that the radius of the sphere is $5m$ . Plug in 5 for the surface area formula for cube, and you will get 150 $m^{2}$ . This number divided by 50 $m^{2}$ would be $\boxed {3}$ .

It is given in the problem that $1~quart=50~m^2$ . So the surface area of the sphere is $6.28~quarts$ converted to $m^2$ . Convert:

$6.28~quarts\left(\dfrac{50~m^2}{1~quart}\right)=314~m^2$

Solve for the radius of the sphere by using the formula: $s=4\pi r^2$ where $s$ is the surface area of the sphere and $r$ is the radius of the sphere. Substitute:

$314=4(3.14)r^2$ $\implies$ $r^2=25$ $\implies$ $r=5$

The formula for the surface area of the cube is $6a^2$ where $a$ is the edge length. Substitute:

$A=6(5^2)=150~m^2$

So the number of quarts needed is $150~m^2\left(\dfrac{1~quart}{50~m^2}\right)=\boxed{3~quarts}$

The surface area of the sphere is,

$S_{A}$ $=$ $6.28 quarts$ ( $\frac{50 m^2}{1 quart}$ ) $=$ $314m^2$

$4pi$ $*$ $r^2$ $=$ $314$

$r$ $=$ $5$

The surface area of the cube is,

$S_{A}$ $=$ $6*5^2$ $=$ $150m^2$

$150m^2$ ( $\frac{1 quart}{50m^2}$ ) $=$ $\boxed{3 quarts}$