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

Solution

It is given that,
Edge of the cube = l
Then, Surface area = 6 (edge)² = 6l²Now, the greatest diameter of hemisphere
= length of an edge of the cube
= l
So, curved surface area of the hemisphere

$equals space 2 space straight pi space open parentheses 1 half close parentheses squared equals space 2 space straight pi space straight l squared over 4 equals πl squared over 2$
And, Area of base of the hemisphere

$equals straight pi space open parentheses l over 2 close parentheses squared equals space straight pi l to the power of italic 2 over 4$

Required surface area
= Surface area of the cubical wooden block – area of the base of the hemisphere + curved surface area of the hemisphere
$equals space 6 l to the power of italic 2 italic minus pi over italic 4 l to the power of italic 2 italic equals italic 6 l to the power of italic 2 italic plus pi over italic 4 l to the power of italic 2$

Some More Questions From Statistics Chapter

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

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Statistics

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

Some More Questions From Statistics Chapter

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