SURFACE AREA OF COMBINED SHAPES

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) + πr

=  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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