18 yds

3 yds

8yds

18f

t6ft

7ft

Surface Area Part 1Work Explain1. Units Changed click

HERE to see2. Simplified parts:

2 rect. 9ft by 24ft 2 rect. 6ft by 7ft 2 rect. 18ft by 7ft 1 half circle w/ radius of

36ft 1 half circle w/ radius of

27ft 1 circumferential

rectangle with radius of 36ft height 24ft

1 circumferential rectangle with radius of 27ft height 24ft

1. To begin, make all units feet, this reduces the number of Decimals Click HERE to see changed

units

2. Next, split the complex shape into simpler shapes (this makes it easier to find area, and reduces chance of mistakes) Additionally, the flat base,

according to the designer, will not count in this diagram for surface area

Also, do not count the bottom of the rectangular prism in the top, it will be found with the circles

Surface Area Part 2Work Explain

3. Rectangle Calculations: 2 x 9ft x 24ft

432ft2

2 x 6ft x 7ft 84ft2

2 x 18ft x 7ft 252ft2

4. Semicircle Calculations: ½[π x (36ft)2]

½(4069.44ft2) 2034.72ft2

½[π x (27ft)2] ½(2289.06ft2) 1144.53ft2

3. Next we will begin by calculating the area of the easier of the pieces, the rectangles. Simply multiply length times

width

4. Next find the area of the half circles Note: for answers to

correspond with the ones shown for π use 3.14 not calculator pi.

You will want to use the area of a circle formula (πr2) however, you will want to divide that by 2 since you have half a circle

Click here for changed

units

Surface Area Part 3Work Explain

5. Circumferential Rectangle calculations: π x 36ft x 24ft

π x 864ft2 2712.96ft2

π x 27ft x 24ft π x 648ft2

2034.72ft2

6. Circular Subtraction 2034.72ft2 - 1144.53ft2

890.19ft2

5. Now we have to find the area of the sides of the cylinders or the circumferential rectangle The formula for the

circumference of a circle times the height will work, you need to make sure you divide it by 2 since you only have half of a cylinder though

6. Looking back, you found the area of a big half circle, however, we need to subtract out the area of the smaller circles to get the answer correct

Click here for changed

units

Surface Area Part 4Work Explain

7. Final Addition The rectangles

432ft2 + 84ft2 + 252ft2

768ft2

Circumferential Rectangles 2712.96ft2 + 2034.72ft2

4747.68ft2

Total including half circle 768ft2 + 4747.68ft2 +

890.19ft2

6405.87ft2

8. Unit Change! 6405.68ft2 / 9ft2

711.76 yd2

7. Next we need to add up all of the parts to find the total surface area

8. 6405.68ft2 is the answer of surface area in feet, but what is it in square yards? Since the feet are smaller

units, and yards are bigger units, you will need to divide in order to get square yards from feet

Remember: 1 square yard is equal to 9 square feet!

711.76 yd2 is the final answer

Click here for changed

units

Volume Part 1Work Explanation

1. Changed Units

2.The base is the semi circle part. The area is: 890.19ft2

1. To begin we are going to switch the units back to feet. Click here to view the image again

2. To find the volume of any three dimensional shape that is not a cone or pyramid, all you must do is find the area of the base and multiply by height.

In this case, we have already found the area of the base of our shape

Volume Part 2Work Explain

3. 809.19ft2 x 24ft 19420.56ft3

4. 6ft x 18ft x 7ft 756ft3

5. 19420.56ft3 – 756ft3

18664.56ft3

6. 18664.56ft3 / 27ft3 691.28yd3

3. Next we need to multiply the area of the base by the height of the object. The height is 24 feet.

4. Next you must count the volume of the cut out rectangular prism on the top of the shape. To find the volume of that prism, multiply length, width, and height together.

5. Next we need to subtract the volume of the rect. prism from the main object

6. Next we need to convert into yards cubed. That will give us the final answer.

Remember 1yd3 is equal to 27ft3

Click here for changed

units

The Final Answers!

The Surface Area is:

711.76 yd2 The Volume is:

691.28yd3