Question

A hemisphere is cut out from one face of a cubical wooden block such that the diameter of the hemisphere is equal to the length of the cube. Determine the surface area of the remaining soild
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Answer 1

Answer:

If a hemisphere is cut out from one face, the surface area of remaining solid = total surface area of cube - base area of hemisphere + lateral surface area of hemisphere

Let the side of cube = a

radius of hemisphere = a/2

TSA of cube = 6a²

base area of hemisphere = π(a/2)² = πa²/4

LSA of hemisphere = 2π(a/2)² = πa²/2

So surface area of remaining solid = 6a² - πa²/4 + πa²/2

= 6a² + πa²/4

= (24a² + πa²) /4

= \frac{24+ \pi}{4}\ a^2

Surface area is \frac{24+ \pi}{4}\ a^2

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