A show-piece shown in figure 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.

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315.23 cm2

215.23 cm2

115.23 cm2

234.23 cm2

answer is A.

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Detailed Solution

To find the total surface area of the figure let us find the surface area of the cube first with length of the edges as 7 cm
We will use the formula of 6a2 and place the value of a as 7 , we get the value of the surface area of the cube as:
The Surface area of 6 sides of cube other than with hemisphere is 6×7×7=294 cm2
The surface area of hemisphere is 2* π * 2.6×2.6=42.45 cm2
The base area of circle of the hemisphere is, π r2 =3.14×2.6×2.6 cm2 =21.22 cm2
Therefore, the total surface area of the figure is given;
Sum of the total surface area of the cube and curved surface of the hemisphere subtracted to area of the circle as:
⇒294 cm2+42.45 cm2−21.22 cm2
⇒315.23 cm2
Hence, The correct answer is option (1).

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