A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the diameter of the hemisphere is equal to the edge of the cube. Determine the volume and total surface area of the remaining block.

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Solution

We have to find the remaining volume and surface area of a cubical box when a hemisphere is cut out from it.

Edge length of cube

Radius of hemisphere

Therefore volume of the remaining block,

So,

So, remaining surface area of the box,

Therefore,

Put the values to get the remaining surface area of the box,

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Q. A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter

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Question 5
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

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