Question

A cylindrical tower surmounted by a cone is built on a cubical plinth of side 14 m. The tower has the maximum base radius and is 21m high. If the height of the cylindrical and conical portion are same, then find the volume of mortar used to make the whole tower. Given, volume of mortar used in 2/7 th of the volume of the whole structure.​

Answer 1

The Given that radius of cone = 12320cm^2.

We know that curved surface area of a cone = pirl.

GIven that curved surface area of a cone = 12320.

pirl = 12320

22/7 * 56 * l = 12320

22 * 8 * l = 12320

176l = 12320

l = 12320/176

= 70.

We know that height of the cone h = \sqrt{l^2 - r^2}

l

2

−r

2

= \sqrt{70^2 - 56^2}

70

2

−56

2

= \sqrt{4900 - 3136}

4900−3136

= \sqrt{1764}

1764

= 42.

Therefore the height of the cone = 42m.

Hope this helps!