Question

If $1$ pint is needed to paint a statue $6$ m high, then the number of pints it will take to paint (to the same thickness) $540$ statues similar to the original but only $1$ m high is

• A. $90$
• B. $72$
• C. $45$
• D. $15$

Answer 1

The correct option is D $15$

The number of pints P of paint needed is proportional to the surface area (hence, to the square of the height h) of a statue and also to the number (n) of statues to be painted. Thus, $p=kn{h}^2$. Substituting $n=1$, $h=6$ and $p=1$ into this equation, we obtain the constant of proportionality $k=\frac{1}{36}$, so that $p=\frac{1}{36}n{h}^2$
Now, when $n=540$, $h=1$, then $p=\frac{1}{36}\times 540\times 1^2=15$.