The figure shows a solid cuboid of dimensions 12 cm by 10 cm by 7 cm, with a half-cylinder of diameter 4 cm horizontally carved out of it. Find: i. the volume of the solid; ii. the total surface area of the solid
Answers
Solid cuboid of dimensions 12 cm by 10 cm by 7 cm, with a half-cylinder of diameter 4 cm horizontally carved out of it.
1. Volume of cuboid = l×b×h
= 12×10×7 cm^3
= 840 cm^3
2. Volume of half cylinder with radius = 2 cm
= 1/2 ( pi×r^2×h )
= 1/2 { pi×2×2×12 }
= 22/7×2×12
= 75.42 cm^3
3. Volume of given solid
= volume of cuboid - volume of half cylinder
= ( 840 - 75.42 ) cm^3
= 764.58 cm^3
4. The total surface area of the solid
= total surface area of cuboid - 1/2× total surface area of cylinder
5. Total surface area of cuboid
= 2 (l×b + b×h + h×l )
= 2( 12×10 + 10×7 +7×12 )
= 2( 120 +70 + 84 )
= 2×274 cm^2
= 548 cm^2
6. TSA of cylinder
= 2×pi×r×( r + h )
= 2×22/7×2×14
= 8×22
= 176 cm^2
7. Surface area of solid
= 548 - 1/2×176
= 548 - 88
= 460 cm^2