Question

A man wants to beautify his front yard by planting four 20−foot-tall palm trees alongside his house. Each tree will need a cylindrical hole that is 34 inches in diameter and 28 inches deep to accommodate the roots. His trash hauler will only take away the excess dirt if it is in rectangular bags that are 2 feet by 1.5 feet by four feet. However, the man can only fill the bags one third of the way or they will be too heavy for him to move. How many bags will he have to buy so he can put all the dirt out for pickup?

Answer 1

He have to buy 4 bags to put all the dirt at once.

Step-by-step explanation:

Radius = 17 inches

Height = 28 inches

Volume of dirt from the cylindrical hole = π(r x r) h

= π(17 x 17) 28

= (3.14) (289) 28

= 25408.88 cubic inches

1 foot = 12 inches

Volume of dirt the bag can hold= 24 x 18 x 48

= 20736 cubic inches of dirt

The man fills only one third of the bag.

The volume of dirt the man fills = (1/3)20736

= 6912 cubic inches

Total bags = 25408.88/6912

= 3.69

= appx. 4 bags

He have to buy 4 bags to put all the dirt at once.