UNIT 1 day 3

-Suface Area-

 Surface area is the total area of the surface of a three-dimensional object.

(surface area examples)

Surface Area of a Cylinder = 2 pi r ² + 2 pi r h

The surface area of a prism = 2 × area of base  +  perimeter of base × H

Pyramid-[Base Area] + ¹/₂ × Perimeter × [Slant Length]

Cone-SA = πr² + πrl

Surface Area of a Sphere = 4 pi r ²

an example of when we would use surface area, is anytime we need to know how much of something will fit into a 3-d figure, such as being a plumber. They need to measure pipes and find the surface rea and volume to know how much water can and will fit. Or also when they checked out the pyramids, they needed to use surface area to know the overall size. Surface area is hugely used in engineering as well.



Here's a practice quiz!
Calculate all surface areas























KEY





Problem one:

For both the front and back faces, l = 5 in. and w = 2 in.

So, the area of the front and back faces is,

5  2  2 = 20 in.²

For both the top and bottom faces, l = 14 in. and w = 5 in.

So, the area of the top and bottom faces is,

14  5  2 = 140 in.²

For both the sides, l = 14 in. and w = 2 in.

So, the area of the two sides is,

14  2  2 = 56 in.²

Add the area of the faces.

20 + 140 + 56 = 216

So, the total surface area of the given solid is 216 in.².

Problem 2:

The triangular prism has triangular bases.

So, to find the area of the bases, use the formula:

Substitute 6 for b and 8 for h.

Therefore, the area of the two bases is,

2(24) = 48 cm²

The triangular prism has rectangular sides.

So, use the formula A = lw to find the area of the sides.

The area of the front side is,

13  8 = 104 cm²

The area of the bottom side is,

13  10 = 130 cm²

The area of the back side is,

13  6 = 78 cm²

Find the sum of the base areas and the area of the sides.

48 + 104 + 130 + 78 = 360

So, the total surface area of the given solid is 360 cm².

Problem three:

The area of the curved surface of a circular cylinder of base radius r and height h is 2πr ·h.

Here, r = 4 and h = 16¹/₆. So, the area of the curved surface is,

2 ·π· 4 · 16¹/₆

To simplify, first write the mixed number as a fraction.

2 ·π· 4 · 16¹/₆ = 2 ·π· 4 ·⁹⁷/₆

Now, multiply.

2 ·π· 4 ·⁹⁷/₆ approx 406.3

So, the area of the curved surface is about 406.3 in.².

he cylinder has circular bases.

So, the area of each base is πr².

Here, r = 4. Therefore, the area of the two bases is,

2(π· 4²)

Simplify.

2 ·π· 4² = 2 ·π· 16  100.5

Add the area of the bases to the area of the curved surface.

406.3 + 100.5 = 506.8

So, the surface area of the given solid is about 506.8 in.