Respuesta :
Answer:
42.5 Cubic Yards
Step-by-step explanation:
To find volume of a rectangle you do length*width*height to get the volume, so 17*15*0.5(because 6 inches is half of a foot) you get 127.5, but they're asking for it in yards not feet so you need to divide 127.5 by 3 and that will give you 42.5.
The volume of the concrete that would be needed in order to make the rectangular foundation for the patio is 1.574 yards³.
What is the Volume of a cuboid?
The volume of the cuboid is the space occupied by the 3D object cuboid. It is the product of the length, width, and depth of the cuboid.
As it is given that we need to make a rectangular foundation, therefore, the shape of the foundation will be a cuboid with sides 5 feet wide, 17 feet long, and depth of 6 inches.
Now, as we know large amounts of concrete can be purchased by the cubic yard only, therefore, we will convert each of the sides of the rectangular foundation into yards.
[tex]\rm Wide, w = 5\ feet = 5 \times \dfrac{1}{3} = \dfrac{5}{3}\ yards\\\\Length, L = 17 feet = 17 \times \dfrac{1}{3} = \dfrac{17}{3}\ yards\\\\Depth, D = 6\ inches = 0.5\ feet = 0.5 \times \dfrac{1}{3} = \dfrac{0.5}{3}\ yards\\\\[/tex]
Now, we know that the volume of the cuboid is given as the product of its length, width, and depth. therefore,
[tex]\text{Volume of Cuboid} = Length\times Width\times Depth[/tex]
[tex]= \dfrac{5}{3} \times \dfrac{17}{3} \times \dfrac{0.5}{3}\\\\= \dfrac{42.5}{27}\\\\=1.574\rm\ yards^3[/tex]
Hence, the volume of the concrete that would be needed in order to make the rectangular foundation for the patio is 1.574 yards³.
Learn more about Volume of Cuboid:
https://brainly.com/question/46030
