Question

a cubical block of side 7 cm is surmounted by a hemisphere what is the greatest diameter the hemisphere can have find the surface area of solid​

Answer 1

Answer:

The greatest diameter=side of the cube=7cm.

The radius of the hemisphere =3.5cm.

Now,

The Surface Area of Solid=Surface Area of Cube - Surface Area of Base Hemisphere + Curve Surface Area of Hemisphere

Surface Area of Cube

=6×side2

=6×7×7

=294sq cm

Surface Area of Base of Hemisphere is,

=πr2

=722×3.52

=38.5cm2

Curved Surface Area of Hemisphere is,

=2×38.5

=77sq cm

∴ total Surface Area is =294−38.5+77

=332.5sq cm.

Answer 2

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It is given that each side of cube is 7 cm. So, the radius will be 7/2 cm.

We know,

The total surface area of solid (TSA) = surface area of cubical block + CSA of hemisphere – Area of base of hemisphere

∴ TSA of solid = 6×(side)2+2πr2-πr2

= 6×(side)2+πr2

= 6×(7)2+(22/7)×(7/2)×(7/2)

= (6×49)+(77/2)

= 294+38.5 = 332.5 cm2

So, the surface area of the solid is 332.5 cm2