Question

Tyler created a fence post by gluing a rectangular prism to the base of a square pyramid. One jar of paint covers an area of 3 square feet. If Tyler does not paint the bottoms of the fence posts, how many jars of paint will he need to paint 6 posts? Explain.

Answer 1

Answer:

404 jars of the paint will be required.

Step-by-step explanation:

From the figure attached,

Lateral area of the fence post = Lateral surface area of the rectangular prism + Lateral surface area of the square pyramid

Lateral surface area of the rectangular prism = Perimeter of the base × height

= (4 × 6) × 48

= 24 × 48

= 1152 square inches

Lateral area of the square pyramid = 4[Area of one lateral side (triangle)]

                                                          = 4[$\frac{1}{2}(\text{Base})(\text{Height})$]

                                                          = 4$[\frac{1}{2}(6)(5)]$

                                                          = 60 square inch

Total lateral area of the fence pots = 1152 + 60

                                                          = 1212 square inch

∵ 3 square inch of the fence post is painted by number of jars of paint = 1

∴ 1 square inch of the fence post will be painted by = $\frac{1}{3}$ jars

∴ 1212 square inch fence post will be painted by = $\frac{1212}{3}=404$ jars

Therefore, 404 jars will be required to paint the fence post.