Ex 12.1 Q2 - 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.
Solution:-Given,
Total height of vessel = 13 cm
Diameter of hemisphere = d = 14 cm
∴ Radius of hemisphere = r =
14
/
2
= 7 cm
It can be observed that radius of the hemispherical part and the cylindrical part is same ( i.e 7 cm ),
∴ Radius of hemisphere = Radius of cylinder = r = 7cm
Height of hemisphere = Radius of hemisphere = 7 cm
∴ Height of cylindrical part, ( h )
= Total height of vessel - Height of hemispherical part
= 13 - 7
= 6 cm
➙ Curved Surface Area ( CSA ) of hemispherical part
= 2πr²
= 2π × ( 7 )²
= 2π × 49
= 98π cm²
➙ Curved Surface Area ( CSA ) of cylindrical part
= 2πrh
= 2π × 7 × 6
= 2π × 42
= 84π cm²
Now,
Inner Surface Area of the vessel is equal to the sum of the Curved Surface Areas of hemispherical part and cylindrical part,
∴ Inner Surface Area of vessel
= CSA of hemispherical part + CSA of cylindrical part
= 98π + 84π
= 182π
= 182 ×
22
/
7
= 26 × 22
= 572 cm²
Hence,
The Inner Surface Area of the vessel is 572 cm².
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Try This..
✒ A solid object is made up of a cone and a hemisphere. The height of the cone is 10 cm and the radius of the hemisphere is 7 cm. Find the total surface area of the solid.
✒ Find the curved surface area of a cone mounted on a hemisphere. The common radius is 5 cm and the slant height of the cone is 12 cm.
✒ A dome on top of a cylindrical building is hemispherical in shape. If the diameter of the dome is 12 m and the height of the cylinder is 30 m, find the total outer surface area of the structure.
✒ A capsule is made by joining two hemispheres to the ends of a cylinder. The total length of the capsule is 15 cm and the radius is 3.5 cm. Find its total surface area.
❌ Common Mistakes
Confusing Diameter with Radius:▸ Always divide diameter by 2 to get the radius.Incorrectly Calculating the Height of the Cylinder:▸ Subtract the radius of the hemisphere from the total height to get the actual height of the cylinder.Using the Wrong Surface Area Formula:▸ Remember, use CSA (not total surface area) since the vessel is hollow.Misapplying the Value of Pi:▸ Stick to 22/7 (as used in NCERT) unless the question specifies otherwise.Not Writing Units:▸ Skipping units or using the wrong ones (like writing volume in cm²).
📝 Related Questions:-
Queries Solved:-
Class 10 Ex 12.1
Ex 12.1 Q2 Class 10
Class 10 Ex 12.1 Q2
Class 10 Chap 12 Ex 12.1 Q2
Class 10 Surface Areas And Volumes
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