Find the surface area and volume of the composite figure.
8 yd2.8 yd4.8 yd3 yd5 yd
The surface area of the composite figure is
yd2.
The volume of the composite figure is
yd3.
To find the surface area of the composite figure, we need to find the areas of all the individual shapes and then sum them up.
1. The first shape is a rectangle with a length of 8 yd and a width of 2.8 yd. The area of this rectangle is given by the formula: Area = length * width = 8 yd * 2.8 yd = 22.4 yd^2.
2. The second shape is also a rectangle with a length of 8 yd and a width of 4.8 yd. The area of this rectangle is: Area = length * width = 8 yd * 4.8 yd = 38.4 yd^2.
3. The third shape is a square with sides of length 3 yd. The area of this square is: Area = side * side = 3 yd * 3 yd = 9 yd^2.
4. The fourth shape is another square with sides of length 5 yd. The area of this square is: Area = side * side = 5 yd * 5 yd = 25 yd^2.
To find the surface area of the composite figure, add up the areas of all the shapes:
Total surface area = 22.4 yd^2 + 38.4 yd^2 + 9 yd^2 + 25 yd^2 = 94.8 yd^2.
Therefore, the surface area of the composite figure is 94.8 yd^2.
To find the volume of the composite figure, we need to find the volumes of all the individual shapes and then sum them up.
1. The first shape is a rectangular prism with length of 8 yd, width of 2.8 yd, and height of 4.8 yd. The volume of a rectangular prism is given by the formula: Volume = length * width * height = 8 yd * 2.8 yd * 4.8 yd = 107.52 yd^3.
2. The second shape is a cube with sides of length 3 yd. The volume of this cube is: Volume = side * side * side = 3 yd * 3 yd * 3 yd = 27 yd^3.
3. The third shape is another cube with sides of length 5 yd. The volume of this cube is: Volume = side * side * side = 5 yd * 5 yd * 5 yd = 125 yd^3.
To find the volume of the composite figure, add up the volumes of all the shapes:
Total volume = 107.52 yd^3 + 27 yd^3 + 125 yd^3 = 259.52 yd^3.
Therefore, the volume of the composite figure is 259.52 yd^3.
To find the surface area and volume of a composite figure, we need to first break it down into simpler shapes and calculate the surface area and volume of each shape. Then, we sum up the surface areas and volumes of all the shapes to get the total surface area and volume of the composite figure.
In this case, the composite figure is made up of a rectangular prism and a pyramid.
1. Rectangular Prism:
The base of the rectangular prism is 8 yd by 4.8 yd, and the height is 3 yd. To find the surface area of a rectangular prism, we can use the formula: SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism.
Plugging in the values, we have:
SA1 = 2(8 yd)(4.8 yd) + 2(8 yd)(3 yd) + 2(4.8 yd)(3 yd).
2. Pyramid:
The base of the pyramid is a rectangle with dimensions of 8 yd by 4.8 yd, and the height of the pyramid is 5 yd. To find the surface area of a pyramid, we use the formula: SA = lw + l√((w/2)^2 + h^2) + w√((l/2)^2 + h^2), where l is the length, w is the width, and h is the height of the pyramid.
Plugging in the values, we have:
SA2 = (8 yd)(4.8 yd) + (8 yd)√((4.8 yd/2)^2 + (5 yd)^2) + (4.8 yd)√((8 yd/2)^2 + (5 yd)^2).
Now, we can calculate the surface area of the composite figure by summing up the surface areas of the rectangular prism and the pyramid: SA = SA1 + SA2.
To calculate the volume of the composite figure, we calculate the volume of the rectangular prism and the pyramid separately:
1. Rectangular Prism:
The volume of a rectangular prism is given by the formula: V = lwh, where l is the length, w is the width, and h is the height. Plugging in the values, we have:
V1 = (8 yd)(4.8 yd)(3 yd).
2. Pyramid:
The volume of a pyramid is given by the formula: V = (1/3)Bh, where B is the base area and h is the height of the pyramid. The base area of our pyramid is (8 yd)(4.8 yd), and the height is 5 yd. Plugging in the values, we have:
V2 = (1/3)(8 yd)(4.8 yd)(5 yd).
Now, we can calculate the volume of the composite figure by summing up the volumes of the rectangular prism and the pyramid: V = V1 + V2.
By plugging in the values and performing the calculations, you will find the surface area and volume of the composite figure.