A hemispherical depression of the hemisphere is cut out from one face of a cubical wooden block of edge 21 cm , such that diameter of the hemisphere is equal to the edge of the cube. Find volume and total surface area of remaining block.
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Hey mate!!!
Here is the answer to your question
Side of cubical wooden block = 21 cm
Diameter of hemispherical = 21 cm
Radius of hemisphere = 10.5 cm
Volume of cubical wooden block having hemispherical depression = volume of cube - volume of hemisphere
= (s)^3 - 2/3¶r^3
= 21 ^3 - 2/3×22/7×10.5×10.5×10.5
= 9261 - 22×10.5 ×10.5
= 9261 - 2425.5
= 6835.5 cm^3
TSA of remaining block = (TSA of cube + CSA of hemisphere) - area of circle
= [6(s)^2 + 2¶r^2] - ¶r^2
= [6×(21) ^2] + ¶r^2
= 6×441 + (22/7×10.5 ×10.5)
= 2646 + (22×1.5×10.5)
= (2646 + 346.5) cm^2
= 2992.5 cm^2
If it is correct, then let me know by marking it as the brainliest.
Regards
Rhea
Here is the answer to your question
Side of cubical wooden block = 21 cm
Diameter of hemispherical = 21 cm
Radius of hemisphere = 10.5 cm
Volume of cubical wooden block having hemispherical depression = volume of cube - volume of hemisphere
= (s)^3 - 2/3¶r^3
= 21 ^3 - 2/3×22/7×10.5×10.5×10.5
= 9261 - 22×10.5 ×10.5
= 9261 - 2425.5
= 6835.5 cm^3
TSA of remaining block = (TSA of cube + CSA of hemisphere) - area of circle
= [6(s)^2 + 2¶r^2] - ¶r^2
= [6×(21) ^2] + ¶r^2
= 6×441 + (22/7×10.5 ×10.5)
= 2646 + (22×1.5×10.5)
= (2646 + 346.5) cm^2
= 2992.5 cm^2
If it is correct, then let me know by marking it as the brainliest.
Regards
Rhea
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