Answer:
Explanation:
The surface area for each rectangle shaped pillow is 552 square inches. I got this by using the formula for finding the surface area for a rectangular prism. [SA= 2 (wl+hl+hw)]. The equation I got was SA= 2( 216+36+24 ). When I solved this equation, I got the surface area of 1 pillow to be 552 sq ft.
The surface area for each cylinder shaped pillow is 835.7 square inches. I got this because the formula for finding the length because the formula for finding the surface area of a cylinder is 2pi (r) (h) + 2pi (r^2). When I substitute the height and the radius in, I will get 2 pi (7) (12) + 2 pi (7^2). When you solve this equation, you can see that the surface area of each cylinder shaped pillow is approximately 835.66 square inches. However, I rounded the .66 to .7. So, the surface area for each cylinder is approximately 835.7 square inches.
The surface area for each sphere shaped pillow is 1256.6 square inches. I got this because the formula for finding the surface area of a sphere is 4 pi (r^2). When you substitute the radius into the equation you will get 4pi (100). When you solve this, you will get approximately 1256.64 square inches. When you round it down, you will find out that the surface area of one cylinder is approximately 1256.6 square inches.
The total surface area of all the pillows will be 4584 square inches. I got this because all we have to do is multiply the surface area of the rectangle pillow by 3, multiply the surface area of a cylinder shaped pillow, then add the surface area of one sphere shaped pillow. The equation you will get will be (552)(3) + (835.7)(2) + 1256.6. When you solve this equation, you will get 4584 square inches.
The volume for each rectangle shaped pillow is 432 cubic inches. I got this because the formula for finding the formula for each rectangle shaped pillow is lwh = V. When I substitute the lengths into the equation, I get that the volume for each rectangle shaped pillow will be 432 cubic inches. (12)(18)(2) =432.
The volume for each cylinder shaped pillow is 1847.3 cubic inches. I got this because the formula for finding the volume of each cylinder is pi (r^2) (h). When I substitute the values that are given, I will get the equation to be 588 pi. When I solve this, I get the volume of the cylinder to be approx. 1847.26 cubic feet or, when rounded, 1847.3 cubic inches. So, the volume of each cylinder shaped pillow is about 1847.3 cubic feet.
The volume for each sphere shaped pillow is 4188.8 cubic inches. I got this because the formula for finding the volume of the sphere is 4 pi r^2. When I substituted the radius in, I got the equation to be 400 pi. When I solved this, I got that the volume of the sphere is 4188.79 cubic inches or 4188.79. So, the volume for one sphere shaped pillow is approximately 4188.8 cubic inches.
The total volume needed to stuff all of the pillows is 9179.3 cubic inches. I got this because there are 3 rectangle shaped pillows (432), 2 cylinder shaped pillows (1847.3), and one sphere (4188.8). Now, I can make the equation to find how much volume is needed to stuff the pillows. The equation is (432)(3) + (1847.3)(2) + (4188.8). When you solve this equation, you get that the total volume needed to stuff all the pillows to be 9179.3 cubic inches. So, the total volume needed to to stuff all of the pillows is 9179.3 cubic inches.