Question

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Answer 1

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

For cubical portion:

Each edge= 6 cm

For hemispherical portion:

Diameter= 4.2 cm

Radius(r)= 4.2/2= 2.1 cm

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

= 6 (6)²= 6 × 36= 216 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= 216- πr² + 2πr²

= 216+πr²

= 216 + (22/7) × 2.1× 2.1

= 216 + 13.86 = 229.86cm²

Hence,total surface area of the decorative block=229.86 cm²

.Now, volume of the block = volume of cube + volume of hemisphere

= (side)3 + (2/3)πr3

= (6)3 + (2/3)(3.14)(2.1)3

= 235.38 cm3
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HOPE THIS WILL HELP YOU.....

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Answer 2

Heya

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Volume of a hemisphere having radius r is = 2/3 ( π × r³ )

And

Volume of cube having edge length a is = a³

=>

Volume of solid = volume of hemisphere + volume of cube

Volume of solid =

2/3 ( 22/7 ) × (2.1)³ + 6³

=>

Volume of solid = 19.404 + 216

=>

Volume of solid = 235.404cm³