What is the volume of the composite figure?

Question

Shape1: Height3 Length3 Width3
Shape2: Height4 Length11 Width3

in.3

Answer 1

To find the volume of the composite figure, we first need to calculate the volume of each individual shape and then add them together.

Shape1:
Volume = Height x Length x Width
Volume = 3 x 3 x 3
Volume = 27 in^3

Shape2:
Volume = Height x Length x Width
Volume = 4 x 11 x 3
Volume = 132 in^3

Now, add the volumes of the two shapes together:
Total Volume = 27 in^3 + 132 in^3
Total Volume = 159 in^3

Therefore, the volume of the composite figure is 159 in^3.

Answer 2

What is the area of the composite figure?
Shape1: Height7 Length16 Width7

Shape2: Height7 Length16 Width7

Shape3: Height7 Length8 Width10

in.3

Answer 3

To find the total surface area of the composite figure, we need to calculate the surface area of each individual shape and then add them together.

Shape 1:
Surface Area = 2[(Length x Width) + (Height x Length) + (Height x Width)]
Surface Area = 2[(16 x 7) + (7 x 16) + (7 x 7)]
Surface Area = 2[112 + 112 + 49]
Surface Area = 2[273]
Surface Area = 546 in^2

Shape 2:
The surface area of Shape 2 will be the same as Shape 1 since they have the same dimensions.
Surface Area = 546 in^2

Shape 3:
Surface Area = 2[(Length x Width) + (Height x Length) + (Height x Width)]
Surface Area = 2[(8 x 10) + (7 x 8) + (7 x 10)]
Surface Area = 2[80 + 56 + 70]
Surface Area = 2[206]
Surface Area = 412 in^2

Total Surface Area = 546 in^2 (Shape 1) + 546 in^2 (Shape 2) + 412 in^2 (Shape 3)
Total Surface Area = 1504 in^2

Therefore, the total surface area of the composite figure is 1504 in^2.