SURFACE AREA & VOLUME

What is Surface Area? Surface Area is the area of each surface of the figure You will have to find the area of each side of the figure and add them together NOTE: all measurements will be squared!!! (since it’s area)

There are 6 rectangles in this prism. Find the area of all & add. Surface Area Example There are 6 rectangles in this prism. Find the area of all & add. 13 in. 12 in. 11 in. 2 rectangles: A= L x W A= 13 x 11 A= 143 in.2 2 rectangles: A= L x W A= 12 x 11 A= 132 in.2 2 rectangles: A= L x W A= 13 x 12 A= 156 in.2 143 + 143 + 132 + 132 + 156 + 156 = 862 in.2

Practice Problem 2 Find the surface area of the triangular prism shown to the right. Find the area of each shape and add. Area of the triangle #1 A = ½ bh A = ½ (12)(16) A = 96 cm2 Area of the triangle #2 A = ½ bh A = ½ (12)(16) A = 96 cm2 Area of the rectangle #1 A = L x W A = 20 (10) A = 200 cm2 Area of the rectangle #2 A = L x W A = 16 (10) A = 160 cm2 Area of the rectangle #3 A = L x W A = 12 (10) A = 120 cm2 SA = 96 + 96 + 200 + 160 + 120 SA = 672 cm2

Practice Problem 3 Find the surface area of the cylinder. There are 2 circles and 2 rectangles in a cylinder 2 circles: A = r2 A = 62 A = 36 A = 113.04 2 “rectangles”: A = rh A = (6)(18) A = 108 A = 339.12 Surface Area = 113.04 + 113.04 + 339.12 + 339.12 = 904.32 in.2

What is Volume? Volume is the measure of the capacity of a container. It is the measure of how much a container of a particular shape will hold - liquids, dry substances, etc.

Cubic Units Volume is measured in cubic units. Use cubes to fill a rectangular prism such as a box.

A unit might be measured in inches, feet, centimeters, etc. One Cubic Unit 1 unit (length) A unit might be measured in inches, feet, centimeters, etc. 1 unit (height) 1 unit (width) Note: All measurements will be cubed! 14in.3

How many cubic units is this rectangle? What did you find? Yes, it is 8 cubic units!

How about this one? Yes! There are 12 cubic units! Remember… there are some cubes you can’t see! Yes! There are 12 cubic units!

The formula for finding the volume of a rectangle is …. What’s the formula? The formula for finding the volume of a rectangle is …. Volume = L x W x H This means we take the length times the width, then multiply that by the height.

Let’s try it! L = 3 H = 3 W = 2 3 x 3 x 2 = 18 cubic units

The Volume Of A Triangular Prism. Consider the triangular prism below: 5cm 8cm The formula for the volume of a triangular prism is : V = ½ b h l B= base h = height l = length Calculate the volume: Volume = ½ b h l V = ½ (5)(5)(8) V = 100 cm3

The Volume Of A Cylinder. Consider the cylinder below: 4cm 6cm The formula for the volume of a cylinder is: V =  r 2 h r = radius h = height. Calculate the volume: V =  r 2 x h V =  x 2 x 2 x 6 V = 75.36 cm3

What Goes In The Box ? 2 Calculate the volume of the shapes below: (2) (1) 16cm 14cm (3) 6cm 12cm 8m 2813.4cm3 30m3 288cm3