To find the volume of the composite figure, we first need to find the volume of each individual prism and then add them together.
Volume of rectangular prism:
Volume = length x width x height
Volume = 14 cm x 5 cm x 4 cm
Volume = 280 cm^3
Volume of triangular prism:
To find the volume of a triangular prism, we need to find the area of the base triangle first. The base triangle is a right triangle with base 5 cm, height 4 cm, and hypotenuse 6 cm (since the distance from the apex to the base is 6 cm).
Base area = 0.5 x base x height
Base area = 0.5 x 5 cm x 4 cm
Base area = 10 cm^2
Now, we can find the volume of the triangular prism using the base area and the length of 14 cm.
Volume = base area x length
Volume = 10 cm^2 x 14 cm
Volume = 140 cm^3
Now, add the volumes of the rectangular prism and the two triangular prisms:
Total volume = 280 cm^3 + 2(140 cm^3)
Total volume = 280 cm^3 + 280 cm^3
Total volume = 560 cm^3
Therefore, the volume of the composite figure is 560 cm^3.
An illustration shows a rectangular prism joined two triangular prisms on either side. The illustration shows two identical triangular prisms, each with one side attached to the length of the rectangular prism. The sides attached to the rectangular prism are oriented such that the triangular prisms are mirror images of one another. The length of the rectangular prism is 14 centimeters. The width and the height are 5 centimeters and 4 centimeters respectively. The distance from the apex of the triangular prism to the base is 6 centimeters.
Solve for the volume of the composite figure.
Write ur answer in cm^3
3 answers
wrong
I apologize for the mistake in my previous response. Let's correct that.
First, let's find the volume of the rectangular prism:
Volume = length x width x height
Volume = 14 cm x 5 cm x 4 cm
Volume = 280 cm^3
Next, let's find the volume of the triangular prism attached to the rectangular prism:
Base area of the triangle = 0.5 x base x height
Base area = 0.5 x 5 cm x 4 cm
Base area = 10 cm^2
Volume of the triangular prism = base area x length
Volume = 10 cm^2 x 14 cm
Volume = 140 cm^3
Since there are two identical triangular prisms attached to the rectangular prism, the total volume of both prisms would be:
Total volume of the triangular prisms = 2 x 140 cm^3
Total volume = 280 cm^3
Now, add the volume of the rectangular prism and the total volume of the two triangular prisms:
Total volume = 280 cm^3 (rectangular prism) + 280 cm^3 (triangular prisms)
Total volume = 560 cm^3
Therefore, the correct volume of the composite figure is 560 cm^3. Thank you for your patience.
First, let's find the volume of the rectangular prism:
Volume = length x width x height
Volume = 14 cm x 5 cm x 4 cm
Volume = 280 cm^3
Next, let's find the volume of the triangular prism attached to the rectangular prism:
Base area of the triangle = 0.5 x base x height
Base area = 0.5 x 5 cm x 4 cm
Base area = 10 cm^2
Volume of the triangular prism = base area x length
Volume = 10 cm^2 x 14 cm
Volume = 140 cm^3
Since there are two identical triangular prisms attached to the rectangular prism, the total volume of both prisms would be:
Total volume of the triangular prisms = 2 x 140 cm^3
Total volume = 280 cm^3
Now, add the volume of the rectangular prism and the total volume of the two triangular prisms:
Total volume = 280 cm^3 (rectangular prism) + 280 cm^3 (triangular prisms)
Total volume = 560 cm^3
Therefore, the correct volume of the composite figure is 560 cm^3. Thank you for your patience.
1 answer