Q. 23.7( 3 Votes )
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.
Answer :
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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