Question -
Answer -
Given,
Diameter of thehemisphere = 3.5 m
So, the radius of thehemisphere (r) = 1.75 m
Height of the cylinder(h) =┬а14/3┬аm
We know that, volumeof the Cylinder = ╧Аr2┬аh1┬а= V1
V1┬а=╧А(1.75)2┬аx 14/3┬аm3
The volume of thehemispherical bottom =┬а2 ├Ч 2/3 ├Ч 22/7 ├Ч r3┬а= V2
V2┬а=┬а2/3├Ч 22/7 ├Ч 1.753┬аm3
Therefore,
The total volume ofthe vessel (V) = volume of the cylinder + volume of the hemisphere
V = V1┬а+V2
V = ╧А(1.75)2┬аx14/3┬а+ 2/3 ├Ч 22/7 ├Ч 1.753
V = ╧А(1.75)2┬а(14/3+ 2/3 x 1.75)
V = 56.15 m2
Hence, the volume ofthe vessel = V = 56.15 m3
Now,
Internal surface areaof solid (S) = Surface area of the cylinder + Surface area of the hemisphere
S = 2 ╧Аr h1┬а+2 ╧Аr2
S = 2 ╧А(1.75)(143) + 2╧А(1.75)2
S = 70.51 m3
Therefore, theinternal surface area of the solid is 70.51 m3