Math, asked by nikkubhairam2091, 10 months ago

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

Answered by techtro
1

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

Similar questions