Question

A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is 14/3 and the diameter of the hemisphere is 3.5 m. Calculate the volume and the internal surface area of the solid.

Answer 1

Given,

Diameter of the hemisphere = 3.5 m

So, the radius of the hemisphere (r) = 1.75 m

Height of the cylinder (h) = 14/3 m

We know that, volume of the Cylinder = πr² h₁ = V₁

V₁ = π(1.75)² x 14/3 m³

The volume of the hemispherical bottom = 2 × 2/3 × 22/7 × r³ = V₂

V₂ = 2/3 × 22/7 × 1.75³ m³

Therefore,

The total volume of the vessel (V) = volume of the cylinder + volume of the hemisphere

V = V₁ + V₂

V = π(1.75)² x 14/3 + 2/3 × 22/7 × 1.75³

V = π(1.75)² (14/3 + 2/3 x 1.75)

V = 56.15 m²

Hence, the volume of the vessel = V = 56.15 m³

Now,

Internal surface area of solid (S) = Surface area of the cylinder + Surface area of the hemisphere

S = 2 πr h₁ + 2 πr²

S = 2 π(1.75)(143) + 2 π(1.75)²

S = 70.51 m³

Therefore, the internal surface area of the solid is 70.51 m³.