The diameter of the base of a cone is 42 cm and its volume is 12936 cm3.

(a) 28 cm
Let h be the height of the cone.
Diameter of the cone = 42 cm
Radius of the cone = 21 cm

Then, volume of the cone $=\frac{1}{3} \pi r^{2} h$

$=\frac{1}{3} \times \frac{22}{7} \times 21 \times 21 \times h$

$=22 \times 21 \times h$

Therefore,

$22 \times 21 \times h=12936$

$\Rightarrow h=\left(\frac{12936}{22 \times 21}\right)$

$\Rightarrow h=28 \mathrm{~cm}$

Hence, the height of the cone is 28 cm.