Question

A vessel is in the form of a hemispherical bowl, surmounted by a hollow cylinder. The diameter of the hemisphere is $12\text{cm}$ and the total height of the vessel is $16\text{cm}$. Find the capacity of the vessel. (Take $\pi$ = 22/7). Also find the internal surface area of the vessel.

• A. Capacity = $1584{\text{cm}}^3;$ Internal Surface Area = $602.88{\text{cm}}^2$
• B. Capacity = $1684{\text{cm}}^3;$ Internal Surface Area = $612.88{\text{cm}}^2$
• C. Capacity = $1784{\text{cm}}^3;$ Internal Surface Area = $622.88{\text{cm}}^2$
• D. Capacity = $1884{\text{cm}}^3;$ Internal Surface Area = $632.88{\text{cm}}^2$

Answer 1

The correct option is A Capacity = $1584{\text{cm}}^3;$ Internal Surface Area = $602.88{\text{cm}}^2$

The diameter of the hemispherical bowl is $12\text{cm}$
The radius of the hemisphere r=$\frac{12}{2}=6\text{cm}$
The curved surface area of the bowl=$2\pi r^2$
= $2\times 3.14\times 6\times 6\text{cm}$
= $226.08{\text{cm}}^2$
The total height of the vessel is =$16\text{cm}$
The height of the cylindrical part=$(16-6)\text{cm}$
=$10\text{cm}$
The surface area of the cylinder =$2\pi rh$
=$2\times 3.14\times 6\times 10{\text{cm}}^2$
=$376.8{\text{cm}}^2$
The surface area of the vessel = Surface area of the cylinder + Surface area of the sphere
=$(377.14+226.28){\text{cm}}^2$
=$602.88{\text{cm}}^2$