A vessel is a hollow cylinder fitted with a hemispheric

SOLUTION

As per the parameters given in the question, we have

Diameter of the hemisphere = 3.5 m

Radius of the hemisphere (say r) = 1.75 m

Height of the cylinder (say h) = $\frac{14}{3}m$

The volume of the Cylinder = πr² h₁ = V₁

V₁ = π (1.75)² $\times \frac{14}{3}{m}^3$

The volume of two hemispheres, $V_2=2\times \frac{2}{3}\times \frac{22}{7}\times r^3=2\times \frac{2}{3}\times \frac{22}{7}\times {1.75}^3$

Therefore, The total volume of the vessel = volume of the cylinder + volume of the two hemispheres = V

V = V₁ + V₂

V = 56 m³

Therefore, Volume of the vessel = V = 56 m³

Internal surface area of solid (S) = 2 πr h₁ + 2 πr²

S = Surface area of the cylinder + Surface area of the hemisphere

$S=2\pi \left(1.75\right)\left(\frac{14}{3}\right)+2\pi (1.75{)}^2=70.51m^3$

Hence, the internal surface area of the solid = S = 70.51 m³