Find the total surface of this composite figure (NOT in terms of pi).

Question

Find the total surface are of this composite figure (NOT in terms of pi).

https://ibb.co/1JtFQMJs

Answer 1

The simplest way to break down a composite figure like this is to consider each individual surface and add them together. To do this not in terms of pi, you can use pi=3.14 to get a decimal answer.

Let's start with the rectangular prism shape:

The bottom face is a rectangle, which uses the area formula [length * width] - 14 ft * 8 ft = 112 sqft

The front and back faces are also rectangles - 14 ft * 16 ft = 224 sqft

The left and right faces are also rectangles - 8 ft * 16 ft = 128 sqft

The very top face is a circle, which uses the area formula [pi * radius^2] - 3.14 * (4 ft)^2 = 50.24 sqft

The face around the top cylinder (called the lateral surface) uses the area formula [2 * pi * radius * height], which you may notice is the perimeter of the top circle times the height - 2 * 3.14 * 4 ft * 8 ft = 200.96 sqft

The top face of the prism is a little more difficult because of the circular cutout. To approach this, we want to think about it as a full rectangle with a section removed. Intuitively, we can think about it as the area of the rectangle with the removal being minus the area of a circle. In math terms, this will look like

[ (length * width) - (pi * radius^2) ] - ( 8 ft * 14 ft ) - ( 3.14 * (4 ft)^2) = ( 112 sqft ) - ( 50.24 sqft ) = 61.76 sqft

Pay attention to the parentheses here, as the order is important.

To get the total surface area, we just need to add all of the faces together, multiplying the duplicate faces by 2.

112 sqft + 2 * 224 sqft + 2 * 128 sqft + 50.24 sqft + 200.96 sqft + 61.76 sqft = 1128.96 sqft

Answer 2

16(58)=928 (not 924) as pictured in the video.

Answer 3

2(14 x 8) +

2(16 x 8) +

2(14 x 16) +

8(8 x 3.14) = TSA