Q2 of 48 Page 261

A show - piece shown in figure 14.10 is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 7 cm and the hemisphere fixed on the top has diameter 5.2 cm. Find the total surface area of the piece.

Given.


A show - piece is made by mounting a hemisphere on cube


The Diameter of hemisphere is 5.2 cm.


Length of side of cube is 7 cm


Formula used/Theory.


Total surface area of Cube = 6 × side2


Curve surface area of Hemisphere = 2πr2


⇒ As we put hemisphere on Cube


The circle part of hemisphere will attach to cube 1 plane


∴ TSA of show - piece is sum of CSA of hemisphere and TSA of cube subtracted by Area of circle of hemisphere


TSA of show - piece =


CSA of Hemisphere + TSA of cube–Area of circle


= 2πr2 + 6 × side2–πr2


= πr2 + 6 × side2


Diameter = 5.2 cm


Radius = = 2.6


TSA of show - piece = 3.14 × 2.6 × 2.6 + 6 × 7 × 7


= 21.22 + 294


= 315.22 cm2


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