Question

A show piece is made of two solids a cube and hemisphere the base of the block is a cube with 7 cm and the hemisphere 6th standard top has diameter 5.2 cm find the total surface area of the piece
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Answer 1

Answer:

The decorative block is a combination of a cube and the hemisphere.

For cubical portion:

Each edge= 5 cm

For hemispherical portion:

Diameter= 4.2 cm

Radius(r)= 4.2/2= 2.1 cm

Total surface area of the cube= 6 × (edge)²

= 6 (5)²= 6 × 25= 150 cm²

Here the part of the cube where the hemisphere is attached is not included in the surface area.

So the total surface area of the decorative block= total surface area of the cube+ area of base of hemisphere + curved surface area of hemisphere

total surface area of the decorative block= 150 - πr² + 2πr²

= 150 +πr²

= 150 + (22/7) × 2.1× 2.1

= 150 + 13.86 = 163.86cm²

Hence,total surface area of the decorative block=163.86 cm²

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