What is the volume of the solid?

Mathematics

1 answer:

Evgen [1.6K]3 years ago

8 0

9514 1404 393

Answer:

(9√3 -3π/2) ft^3 ≈ 10.88 ft^3

Step-by-step explanation:

The area of the hexagon is given by the formula ...

A = (3/2)√3·s^2 . . . . for side length s

The area of the hexagonal face of this solid is ...

A = (3/2)√3·(2 ft)^2 = 6√3 ft^2

The area of the circular hole in the hexagonal face is ...

A = πr^2

The radius is half the diameter, so is r = (2 ft)/2 = 1 ft.

A = π(1 ft)^2 = π ft^2

Then the area of the "solid" part of the face of the figure is ...

A = (6√3 -π) ft^2

The volume is ...

V = Bh . . . . . where B is the area of the base of the prism, and h is its height

V = ((6√3 -π) ft^2)(3/2 ft) = (9√3 -3π/2) ft^3 ≈ 10.88 ft^3

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