Question

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

Answer 1

Given:

A design for a traffic cone is shown below. In order for it to have a solid foundation, the designers want to make the base and cone out of solid plastic.

If the plastic is $0.75 per cubic cm

To find:

How much will it cost them to make 5 cones?

Solution:

From the given figure, we will find the volume of each such solid plastic cones along with base:

For Conical part:

Height, h = 17 cm

Radius, r = 13 cm

∴ Volume of the cone = $\frac{1}{3} \pi r^2 h = \frac{1}{3} \times 3.14 \times 13^2 \times 17 = 3007.07 \:cm^3$

For Cylindrical base:

Height, h = 2 cm

Radius, r = 2 cm

∴ Volume of the base = $\pi r^2 h = 3.14 \times 13^2 \times 2 = 1061.32 \:cm^3$

Therefore,

The volume of each traffic cone is,

= [Volume of cone] + [Volume of base]

= 3007.07 cm³ + 1061.32 cm³

= 4068.39 cm³

The volume of 5 traffic cones is = 4068.39 cm³ × 5 = 20341.95 cm³

Now,

If 1 cm³ plastic costs = $ 0.75

Then,

20341.95 cm³ plastic will cost = $ 0.75 × 20341.95 cm³ = $ 15256.46

Thus, to make 5 such traffic cone, it will cost them → $ 15256.46.

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