|Class 10 Maths Surface Areas Volumes||Surface Area of Combination of Solids|
Surface Area of Combination of Solids
As seen, we can easily break a complex solid into basic solids.
Total surface area of the complex solid is the sum of the curved surface areas of each of the individual basic parts
Numerical: 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: We can break this vessel into a cylinder & Hemisphere as then find the surface area.
Total inner Surface Area of Vessel = Inner surface area of (Cylinder A + Hemisphere B)
= 2πrh + 2πr2
= 2 * 22/7 * 7 * 6 + 2 * 22/7 * 7 * 7 cm2
= 572 cm2
Note that some part of the surface area may disappear in the process of joining them, thus we can’t blindly add surface area of all the basic solids that forms the complex object. Let’s take one Example.
Numerical: A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
The greatest diameter can be the length of cube that is 7 cm.
Radius = 3.5 cm
Surface Area of Solid = Surface area of (Cube + Hemisphere – Base of Hemisphere)
= 6 (cube side)2 + 2πr2 -πr2
= 6 * 7 * 7 + 2 * 22/7 * 3.5 * 3.5 - 22/7 * 3.5 * 3.5 cm2
= 332.5 cm2
Note that we subtracted the surface area of base of the hemisphere as it got disappeared.