a cubical block of side 7cm is surmounted by a hemisphere. what is the greatest diameter the hemisphere can have? find the surface area of the solid
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The greatest diameter the hemisphere can have is the side of the cube, since the hemisphere is surmounted over the cube.
Hence, greatest diameter of the hemisphere = 7cm
Surface area of the solid
= Area of 5 faces of the cube + Area of the 6th face subtracted by the semicircle part of the hemisphere + curved surface area of the hemisphere
= 5 × 7² + (7² - pi×(7/2)²) + 2×pi×(7/2)²
Value of pi = 22/7 for convenience
= 245 + (49 - 38.5) + 77
= 322 + 10.5
= 332.5 cm²
Hence, the surface area of the solid = 332.5 cm²
Hope this helps...
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