Question

A town is using a storage container in the shape of an inverted cone to
store salt for treating icy roads. If the town needs to store 10,000 cubic
feet of salt, and the cone has a height equal to its diameter, what are the
dimensions of the storage container?
O Height and diameter are both 29.4 feet.
O Height and diameter are both 33.7 feet.
O Height and diameter are both 42.4 feet.
O Height and diameter are both 67.4 feet.

Answer 1

Using the volume of the cone, it is found that:

Height and diameter are both 33.7 feet.

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The volume of a cone with height h and diameter d is given by:

$V = \frac{\pi d^2h}{12} = \frac{3.1415 d^2h}{12}$

In this question:

• Diameter and height equal, thus $d = h$.
• Volume of 10,000 cubic feet, thus $V = 10000$

$10000 = \frac{3.1415h^3}{12}$

$3.1415h^3 = 120000$

$h^3 = \frac{120000}{3.1415}$

$h^3 = 38197.19$

$h = \sqrt[3]{38197.19}$

$h = 33.7$

Thus, both are 33.7 feet.

A similar problem is given at https://brainly.com/question/16717748