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 the solid.​

Answer 1

$\huge \underline \mathbb {SOLUTION:-}$

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

• Figure provided in the above attachment.

We know:

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

Therefore:

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

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Answer 2

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