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 × side^{2}

Curve surface area of Hemisphere = 2πr^{2}

⇒ 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

= 2πr^{2} + 6 × side^{2}–πr^{2}

= πr^{2} + 6 × side^{2}

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 cm^{2}

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