Question

A design for a traffic cone is shown below. In order for it to have a solid foundationthe designers want to make the base and cone out of solid plastic. If the plastic is $0.75per cubic cm, how much will it cost them to make 5 cones? Show all of your work, andapproximate pi using 3.14.)

Answer 1

Given:

Dimensions of the Traffic Cone:

Height of Cone = 17 cm

Radius of Base = 13 cm

Height of Base = 2 cm

Price of Plastic = $0.75 per cubic cm

First, let's determine the volume of the traffic cone.

It composes of a Cone and a Cylindrical Base, to get the volume, we will be using the following formula:

$\text{ Volume = Volume of Cone + Volume of Cylinder = }\frac{1}{3}\pi r^2h\text{ + }\pi r^2h$

We get,

$\text{ Volume = }\frac{1}{3}\pi r^2h\text{ + }\pi r^2h$$\text{ = }\frac{1}{3}(3.14)(13)^2(17)\text{ + (3.14)(13)}^2(2)$$\text{ = }\frac{1}{3}(3.14)(169)^{}(17)\text{ + (3.14)(169)}(2)$$\text{ = }\frac{1}{3}(9,021.22)\text{ + (}1,061.32)$$\text{ = }3,007.07\text{ + }1,061.32$$\text{ Volume = }4,068.39\text{ cu. cm.}$

Therefore, the volume of 1 Traffic Cone is 4,068.39 cubic cm.

The price of 1 Traffic Cone is : 4,068.39 cubic cm. x $0.75 per cubic cm. = $3,051.29

Therefore, the cost of 5 Traffic Cones will be: $3,051.29 x 5 = $15,256.45

In Summary:

Volume of 1 Traffic Cone = 4,068.39 cubic cm.

Price of 1 Traffic Cone = $3,051.29

Cost of 5 Traffic Cones = $15,256.45