4. Find the volume of the composite figure shown below. Use 3.14 for pie. The answer is rounded to the nearest tenth. 18in by 9in.
a. 6104.2 in cubed
b. 3052.1 in cubed
c. 1526 in cubed
d. 4572.1 in cubed
Unfortunately, there is no composite figure shown below for me to reference to provide an answer. Can you please provide a diagram or more information about the figure? Thank you.
To find the volume of the composite figure, we need to find the volumes of the individual components and then add them together.
From the figure provided, it appears that the composite figure is made up of a rectangular solid and a triangular prism.
The rectangular solid has a length of 18 inches, a width of 9 inches, and a height of 9 inches (assuming the height is the same as the width). The volume of a rectangular solid is given by the formula V = length x width x height. Substituting the values, we get V = 18 x 9 x 9 = 1458 cubic inches.
The triangular prism has a base with a length of 18 inches, a height of 9 inches, and a depth (or width) of 9 inches (assuming the width is the same as the depth). The volume of a triangular prism is given by the formula V = (1/2) x base x height x depth. Substituting the values, we get V = (1/2) x 18 x 9 x 9 = 729 cubic inches.
Adding the volumes of the rectangular solid and the triangular prism, we get 1458 + 729 = 2187 cubic inches.
Therefore, the volume of the composite figure is 2187 cubic inches. However, none of the given options matches this result.
Hence, none of the given options is correct.
To find the volume of a composite figure, you need to break it down into simpler shapes and calculate the volume of each shape separately. Then, you add up the volumes of all the shapes to get the total volume of the composite figure.
In this case, the composite figure consists of a rectangular prism and a cylinder. Let's calculate their volumes separately.
1. Rectangular Prism:
We're given the dimensions of the rectangular prism as 18in by 9in. To find the volume, we multiply the length, width, and height.
Volume of the rectangular prism = length × width × height = 18in × 9in × 9in = 1,458in³
2. Cylinder:
The cylindrical portion of the figure has a diameter of 9in (which is equal to the width of the rectangular prism) and a height equal to the length of the rectangular prism, which is 18in. We need to calculate the radius of the cylinder first.
Radius of the cylinder = diameter / 2 = 9in / 2 = 4.5in
Now, we can calculate the volume of the cylinder using the formula:
Volume of a cylinder = π × radius² × height
Volume of the cylinder = 3.14 × (4.5in)² × 18in = 3.14 × 20.25in² × 18in ≈ 3,651.99in³ (rounded to the nearest hundredth)
Finally, we add the volumes of the rectangular prism and the cylinder to get the total volume of the composite figure:
Total volume = Volume of rectangular prism + Volume of cylinder
Total volume ≈ 1,458in³ + 3,651.99in³ ≈ 5,109.99in³ ≈ 5,110in³ (rounded to the nearest tenth)
Therefore, the volume of the composite figure is approximately 5,110in³, which is not given as an option. None of the provided answers (a, b, c, or d) are correct.