18 yds 3 yds 18ft 6ft 7ft

Surface Area Part 1 Work Explain 1. Units Changed click HERE to seeHERE 2. 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 unitsHERE 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

54 ft 9 ft 24ft 18ft 6ft 7ft

Surface Area Part 2 Work Explain 3. Rectangle Calculations: 2 x 9ft x 24ft 432ft 2 2 x 6ft x 7ft 84ft 2 2 x 18ft x 7ft 252ft 2 4. Semicircle Calculations: ½[π x (36ft) 2 ] ½( ft 2 ) ft 2 ½[π x (27ft) 2 ] ½( ft 2 ) ft 2 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 (πr 2 ) however, you will want to divide that by 2 since you have half a circle Click here for changed units

Surface Area Part 3 Work Explain 5. Circumferential Rectangle calculations: π x 36ft x 24ft π x 864ft ft 2 π x 27ft x 24ft π x 648ft ft 2 6. Circular Subtraction ft ft ft 2 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 4 Work Explain 7. Final Addition The rectangles 432ft ft ft 2 768ft 2 Circumferential Rectangles ft ft ft 2 Total including half circle 768ft ft ft ft 2 8. Unit Change! ft 2 / 9ft yd 2 7. Next we need to add up all of the parts to find the total surface area ft 2 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! yd 2 is the final answer Click here for changed units

Volume Part 1 Work Explanation 1. Changed Units 2. The base is the semi circle part. The area is: ft 2 1. To begin we are going to switch the units back to feet. Click here to view the image againhere 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 2 Work Explain ft 2 x 24ft ft ft x 18ft x 7ft 756ft ft 3 – 756ft ft ft 3 / 27ft yd 3 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 1yd 3 is equal to 27ft 3 Click here for changed units

The Final Answers! The Surface Area is: yd 2 The Volume is: yd 3