Question

A cone-shaped building has a height of 11.4 meters and a base with a diameter of 12 meters. The building will be filled with road salt that costs $20 per cubic meter. How much will it cost to fill the building with road salt? Use 3.14 for π

Answer 1

The cost to fill the building with road salt is $ 8591.04

Solution:

Given that, A cone-shaped building has a height of 11.4 meters and a base with a diameter of 12 meters

Therefore,

Height = 11.4 meters

diameter = 12 meters

$radius = \frac{diameter}{2} = \frac{12}{2} = 6$

radius = 6 meters

Let us first find the volume of cone

The volume of cone is given as:

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

Where, "V" is the volume of cone

"h" and "r" are height and radius of cone

Substituting the given values, we get

$V = \frac{3.14 \times 6^2 \times 11.4}{3}\\\\V = 3.14 \times 12 \times 11.4\\\\V = 429.552$

Thus volume of cone is 429.552 cubic meters

The building will be filled with road salt that costs $20 per cubic meter

1 cubic meter = $ 20

Therefore, for 429.552 cubic meters, we get,

$cost = 20 \times 429.552\\\\cost = 8591.04$

Thus cost to fill the building with road salt is $ 8591.04