#### Answer

(a) $P=ks^{3}$
(b) $k=0.08$, $P=0.08s^3$
(c) $P=270\ $hp

#### Work Step by Step

(a) Since $P$ is directly proportional to the cube of $s$, we have:
$P=ks^{3}$
(b) We are given: $P=80$ and $s=10$, so we have:
$80=k(10)^{3}$
$k=\frac{80}{1000}=0.08$
Therefore:
$P=0.08s^3$
(c) We are given $s=15$ and need to find $P$:
$P= 0.08(15)^{3}=270\ $hp