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Thesurface areaof a solid object is a measure of the totalareathat thesurfaceof an object occupies.

Surface Area of Solids

SA = wh + lw + lh + lsThe variables in this formula stand for:

Surface Area of a right triangular prism

Find the surface area of this right triangular prism. Dimensions are in feet.

SA = wh + lw + lh + lsSA = 5(6)+9(5)+9(6)+9(7)SA = 30+45+54+63SA = 192 ft

Surface Area of a right triangular prism

Thesurface areaof a cube with side s is:SA=6s2

Surface Area of A Cube

To find the surface area of a rectangular prism, add the areas of its flat surfaces:

Area of top and bottom rectangles (bases) area of left, right, front and back rectangles (lateral areas)Surface Area of A Rectangular Prism

Thesurface areaof a rectangular prism is the area of 2 bases + sum of the areas of the lateral faces.

SA=2B+LA

Example:Find the surface area of a rectangular prism whose length is 7cm, width 4cm, and thickness, 5cm.

2 bases2x(7x4)=564 lateral faces2x(5x7)=702x(5x4)=40 166cm2

Surface Area of A Regular Square PyramidA square pyramid is a polyhedron with a square base and 4 triangular faces. All the triangular faces meet at a single point called the apex. The faces of the pyramid connect the bases with the apex. Surface Area of a Square Pyramid is the sum of the surface area of the square base and the surface area of the 4 triangular faces.

The surface area of a cylinder can be found by breaking it down into three parts:The two circles that make up the ends of the cylinder.The side of the cylinder, which when "unrolled" is a rectangle

A cylinder has a radius of 13 cm and a height of 22 cm. Find it's surface area.Solution:In this problem:r = 13 cmd = 26 cmh = 22 cmpi = 3.14SA = 2r2+ 2rhSA = 2()(132) + 2[()(13)(22)]SA = 1061.858 + 1796.991SA = 2858.85 cm2

Surface area of a right circular cone

The first step in finding the surface area of a cone is to measure the radius of the circle part of the cone. The next step is to find the area of the circle, or base. The area of a circle is pi times the radius squared (r2). Now, you will need to find the area of the cone itself. In order to do this, you must measure the side (slant height) of the cone.

You can now use the measurement of the side to find the area of the cone. The formula for the area of a cone is pi times the radius times the side (rl).

So the surface area of the cone equals the area of the circle plus the area of the cone and the final formula is given by:

SA = r2+ rl

Example:

Find the total surface area of a right cone if the radius is 6 inches and the slant height is 10 inches.

T. S. A. = (6)2+ (6)(10) = 36 + 60 301.59 inches2

Surface Area of a Sphere

The surface area of a sphere of radius 'r' is given by:surface area = 4r2NOTE: The value ofpcan never be known exactly, so surface areas of spheres cannot be calculated exactly. Common approximations forpare: 3.14, and22/7.

Exercises:Find the surface of area of the ff. solids: 2) A cube with s= 2.2 cm.

2) A cylinder with h=15 cm, r=3.2 cm

3) A rectangular prism with L=12cm, w=7cm,and h=6cm.

4) A square pyramid with side (b) = 4.2cm, slant height (s) = 7cm.

5) A sphere with radius of 2.5 cm.

6) A cone with r=5cm, l=12 cm (slant height)

7) A cube with S= 0.9m

8) A rectangular pyramid with L=5cm, w=3.3cm, h=9cm (slant h. Assume that slant h is equal in all 4 sides of the pyramid.

Day 2Evaluation: Find the surface area of the ff:

1)2)

3)4)

5) Find the surface area of a square pyramid with base length 3cm and vertical height 5cm.

Hint: use Pythagorean theorem to solve for slant height.

6) A spherical ball has a surface area of 2464 cm2. Find the radius of the ball.

Assignment

Research and review about volume of solids.