Question

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel​

Answer 1

$\huge \underline \mathbb {SOLUTION:-}$

The diagram is as follows:

• Refer to the above attachment.

Now, the given parameters are:

The diameter of the hemisphere = D

⠀⠀⠀⠀⠀⠀⠀= 14 cm

The radius of the hemisphere = r

⠀⠀⠀⠀⠀⠀⠀= 7 cm

Also, the height of the cylinder = h

⠀⠀⠀⠀⠀⠀⠀⠀= (13 - 7) = 6 cm

And, the radius of the hollow hemisphere = 7 cm

Now,

• The inner surface area of the vessel = CSA of the cylindrical part + CSA of hemispherical part

➠ (2πrh+2πr²) cm²

➠ 2πr(h+r) cm²

➠ 2 × 22/7 × 7 (6+7) cm²

➠ 572 cm²

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

Answer 2

Now, the given parameters are:

The diameter of the hemisphere = D = 14 cm

The radius of the hemisphere = r = 7 cm

Also, the height of the cylinder = h = (13-7) = 6 cm

And, the radius of the hollow hemisphere = 7 cm

Now, the inner surface area of the vessel = CSA of the cylindrical part + CSA of hemispherical part

(2πrh+2πr2) cm2 = 2πr(h+r) cm2

2×(22/7)×7(6+7) cm2 = 572 cm2