The area of a triangle is given by
... A = (1/2)bh
where b is the length of the base and h is the height perpendicular to the base. For your right triangle, the area is
... A = (1/2)(4 m)(7 m) = 14 m²
The area of a circular sector is given by
... A = (1/2)r²·sin(α)
where r is the radius and α is the angle in radians. For your sector, the area is
... A = (1/2)(4 m)²sin(60°) = 4√3 m²
Then the area of the base of your cylinder is the sum of these, ...
... B = (14 + 4√3) m²
The volume of a cylinder is the product of its base area and height.
... V = Bh
For your cylinder, that volume is
... V = ((14 +4√3) m²)·(8 m)
... V = (112 +32√3) m³ ≈ 167.43 m³
