Find the surface area :
Example 1 :
Solution :
In the given picture, we have a cuboid and a triangular prism.
Surface area of cuboid = 2(lb+bh+hl)
l = 19 ft, b = 9 ft and h = 11 ft
= 2(19x9 + 9x11 + 11x19)
= 2(171+99+209)
= 2(479)
= 958 square feet
Surface area of triangular prism = 2(area of front and back face) + 2(area of side faces)
= 2(1/2) ⋅ 12 ⋅ 10 + 2(13⋅9)
= 120+234
= 354 square feet
= 958+354
= 1312
Now at the top, we have to ignore the base area of triangular prism.
= 1312 - (10 x 9)
= 1312 - 90
= 1222 square feet
So, the required surface area of the picture given above is 1222 square feet.
Example 2 :
Solution :
Surface area of the shape = Curved surface area of cone + Curved surface area of hemisphere
= π rl + 2πr2
Slant height = √r2+h2
l = √52+122
l = √(25+144)
l = 13
= π r(l+2r)
= 3.14 ⋅ 5(13+2(5))
= 3.14 ⋅ 5(23)
= 361.1 square yard
Example 3 :
Solution :
Surface area of the given picture = Total surface area of cuboid - Curved surface area of base of hemisphere + curved surface area of hemisphere
= 2(lb+bh+hl) - πr2 + 2πr2
= 2(lb+bh+hl) + πr2
= 2 (36+60+60) + 3.14(2.5)2
= 2 (36+60+60) + 3.14(2.5)2
= 312 + 19.625
= 331.63 square yards.
Example 4 :
Solution :
Required area = Total surface area of rectangular prism at the top - Base area of top rectangular prism + area rectangular prism at the top (5 sides)
= 2(135+45+75) - 54 + (54+54+54+36+36)
= 2(255) - 54 + 234
= 510 - 54 + 234
= 690 square inches
Example 5 :
Solution :
Required area = Area of 5 sides of cube + Area of triangular prism with square base
= 5 (13 ⋅ 13) + 4 (1/2 ⋅ 13 ⋅ 12)
= 5 (169) + 2(156)
= 845 + 312
= 1157 square inches.
Example 6 :
Solution :
Required area = Curved surface area of cylinder + surface area of 2 hemispheres
= 2π rh + 2 (2πr2)
= 2πr(h+2r)
= 2 (3.14) 3 (9+6)
= 18.84 (15)
= 282.6 square feet
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