Solve for the volume of the composite figure.
(1 point)
Responses
616 cm3
616 cm cubed
448 cm3
448 cm cubed
154 cm3
154 cm cubed
952 cm3
To find the volume of a composite figure, we need to break down the figure into simpler shapes and then find the volume of each shape separately.
We see that the composite figure consists of a rectangular prism and a pyramid attached to the rectangular base.
The volume of the rectangular prism can be calculated using the formula:
Volume = length x width x height
Given that the dimensions of the rectangular prism are:
Length = 8 cm
Width = 7 cm
Height = 11 cm
Volume of the rectangular prism = 8 cm x 7 cm x 11 cm
Volume of the rectangular prism = 616 cm^3
Next, the volume of the pyramid can be calculated using the formula:
Volume = 1/3 x base area x height
The base of the pyramid is a rectangle with dimensions 8 cm x 7 cm. The area of the base can be calculated as:
Base Area = length x width
Base Area = 8 cm x 7 cm
Base Area = 56 cm^2
Given that the height of the pyramid is 4 cm.
Volume of the pyramid = 1/3 x 56 cm^2 x 4 cm
Volume of the pyramid = 75.33 cm^3
Therefore, the total volume of the composite figure is:
Total Volume = Volume of rectangular prism + Volume of pyramid
Total Volume = 616 cm^3 + 75.33 cm^3
Total Volume = 691.33 cm^3
Therefore, the correct answer is not provided in the options.