Work out the surface area of the figure given below (use π= 3.14).
Solution:
Let us construct the given figure as shown below.
The Total Surface Area = Surface Area of cuboid A + Surface Area of Cuboid B + Surface Area of Cuboid C + Surface Area Cuboid D + Surface Area of Cuboid D
Surface Area of Cuboid A = 2 × (5 × 18 + 5 × 18 + 18 × 18) - 18 × 18
Surface Area of Cuboid A = 2 × (90 + 90 + 324) - 324 = 2 × (504) - 324 = 684cm²
Surface Area of Cuboid B = 2 × (18 × 8 + 2 × 18 + 2 × 8) - 2 × 18 - 18 ×8
Surface Area of Cuboid B = 2 × (144 + 36 + 16) - 36 - 144 = 2 × 196 - 36 - 144 = 212cm²
Surface Area of Cuboid C = 2 × (18 × 3 + 3 × 5 + 18 × 5) - 18 × 2 - 18 × 3
Surface Area of Cuboid C = 2 × (54 + 15 + 90) - 36 - 54 = 318 - 36 - 54 = 228cm²
Surface Area of Cuboid D = 2 × (3 × 18 + 18 × 18 + 3 × 18) - 18 × 18 - 18 × 3
Surface Area of Cuboid D = 2 × (54 + 324 + 54) - 324 - 54 = 486cm²
Surface Area of Cuboid E = 2 × (8 × 18) = 288 cm²
Total Surface Area = 684 + 212 + 228 + 486 + 288 = 1898cm²
✦ Try This: Work out the surface area of the figure given below (use π= 3.14)
The Total Surface Area = Surface Area of cuboid A + Surface Area of Cuboid B + Surface Area of Cuboid C + Surface Area Cuboid D + Surface Area of Cuboid D
Surface Area of Cuboid A = 2 × (3 × 15 + 3 × 15 + 15 × 15) - 15 × 15
Surface Area of Cuboid A = 2 × (45 + 45 + 225) - 225 = 2 × (315) - 225 = 405cm²
Surface Area of Cuboid B = 2 × (15 × 6 + 1 × 15 + 1 × 6) - 1 × 15 - 15 × 6
Surface Area of Cuboid B = 2 × (90 + 15 + 6) - 15 - 90 = 2 × 111 - 15 - 90 = 117cm²
Surface Area of Cuboid C = 2 ×(15 × 2 + 3 × 5 + 18 × 5) - 18 × 2 - 18 × 3
Surface Area of Cuboid C = 2 × (54 + 15 + 90) - 36 - 54 = 318 - 36 - 54 = 228cm²
Surface Area of Cuboid D = 2 × (2 × 15 + 15 × 15 + 2 × 15) - 15 × 15 - 15 × 2
Surface Area of Cuboid D = 2 × (30 + 225 + 30) - 225 - 30 = 315cm²
Surface Area of Cuboid E = 2 × (6 × 15) = 180 cm²
Total Surface Area = 405 + 117 + 228 + 315 + 180 = 1245cm²
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 123
Work out the surface area of the figure given below (use π= 3.14).
Summary:
The total surface area of the solid is 1898cm²
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