Question

A stalactite which may be seen hanging in the Endless Caverns of Virginia is approximately in the form of a cone

4 ft long with a base 18 in. in diameter. The calcium carbonate of which it is formed weighs 131 lb per cu. Ft. find

the weight of the stalactite.​

Answer 1

Given:

A stalactite which may be seen hanging in the Endless Caverns of Virginia is approximately in the form of a cone 4 ft long with a base 18 in. in diameter.

The calcium carbonate of which it is formed weighs 131 lb per cu. ft

To find:

The weight of the stalactite

Solution:

The height of the conical stalactite, h = 4 ft

The diameter of the conical stalactite = 18 in = $\frac{18}{12} \:ft$ = 1.5 ft

So, the radius, r = $\frac{1.5}{2} = 0.75\: ft$

∴ The volume of the conical stalactite is,

= $\frac{1}{3} \pi r^2 h$

= $\frac{1}{3} \times \frac{22}{7} \times 0.75^2 \times 4$

= $\bold{2.357 \:ft^3}$

Now,

If 1 cubic ft of calcium carbonate weighs = 131 lb

Then,

2.357 ft³ of calcium carbonate will weigh = 2.357 × 131 = 308.76 lb

Thus, the weight of the conical stalactite is → 308.76 lb.

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