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A project requires a round, concrete patio on the back of a house with a diameter of 24′. How much concrete would be required to pour the patio 6″ thick? Express your answer in cubic yards.

Sagot :

semsee45

Answer:

8.38 yd³

Step-by-step explanation:

Use volume of a cylinder formula: [tex]\pi r^2h[/tex]

where r is the radius and h is the height.

Radius = half of diameter = 24 ÷ 2 = 12 ft

Height = 6 in

We need to express the answer in yards, so first convert radius and height to yards:

1 yard = 3 ft = 36 in

⇒ Radius = 12 ft = 4 yards

⇒ Height = 6 in = 1/6 yards

Substituting these values into the volume of a cylinder formula:

[tex]\pi r^2h[/tex] = [tex]\pi[/tex] x 4² x 1/6

       =   [tex]\frac{8}{3} \pi[/tex]

       = 8.38 yd³ (nearest hundredth)

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