Question

Find the surface area of the composite solid. Round your answer to the nearest hundredth.

Answer 1

Answer: The surface area of the composite solid is 529.7 cm².

Step-by-step explanation:

Since we have given that

Length of cuboid = 11 ft

Breadth of cuboid = 8 ft

Height of cuboid = 6 ft

There is a cylinder of radius 4 ft and height 5 ft are put over the solid.

So, Surface area of composite solid = 2(bh+lh)+lb+(lb-Area of base of cylinder)

$=2(8\times 6+11\times 6+11\times 8)-\pi r^2+2\pi rh+\pi r^2\\\\=2(48+22+88)+2\pi rh\\\\=2\times 202+2\times \frac{22}{7}\times 4\times 5\\\\=404+125.71\\\\=529.71\ cm^2$

Hence, the surface area of the composite solid is 529.7 cm².

Answer 2

Check the picture below

so.. is really just 6 rectangles and a cylinder hmmm ok.. .so just get the area of each, and sum them up

now... notice the base of the cylinder, is resting on the rectangular prism.... so, they touch each other there, and thus that circular base of the cylinder, is not part of the area, since its inside, not outside

so... once you get all those areas, summed up, you need to "subtract" that circular base, recall the area of a circle is πr², now the radius of the cylinder is r = 4, so that circular area is π4², so, you subtract that from the sum of the others, and that's the surface area of the composite figure