What is the volume of the triangular prism to the nearest whole unit?
A triangular prism is shown. The height of the prism is 16 feet and the triangular bases have a side that is 15 feet in length. A dashed line that is labeled 3 feet is drawn to the opposite vertex from the 15 foot side of one of these triangles. A small square is located at the intersection of this dashed line with the side of the triangular base.
A. 360 ft3
B. 240 ft3
C. 1,440 ft3
D. 720 ft3
To find the volume of a triangular prism, you need to multiply the area of the base by the height of the prism.
The base of the prism is a triangle with a base of 15 feet and a height of 3 feet (the length of the dashed line).
The area of the base is (1/2) x base x height = (1/2) x 15 x 3 = 22.5 square feet.
Multiplying this by the height of the prism (16 feet) gives a volume of 360 cubic feet.
Therefore, the answer is A. 360 ft3.
To find the volume of the triangular prism, we need to multiply the base area of the triangular base by the height of the prism.
The base of the triangular prism is a triangle with a side length of 15 feet. However, we need to find the length of the base using the dashed line and the small square.
Since the dashed line is 3 feet and the length of the triangle side is 15 feet, we can use the Pythagorean theorem to find the length of the base.
Let's call the length of the base x. Using the Pythagorean theorem, we have:
x^2 + 3^2 = 15^2
x^2 + 9 = 225
x^2 = 216
x = √216
x ≈ 14.7 feet
Now we can find the area of the triangular base:
Area = (1/2) * base * height
Area = (1/2) * 14.7 * 15
Area ≈ 110.25 square feet
Finally, we can calculate the volume of the prism:
Volume = base area * height
Volume ≈ 110.25 * 16
Volume ≈ 1764 cubic feet
Rounded to the nearest whole unit, the volume of the triangular prism is approximately 1,764 ft^3.
Therefore, the correct answer is C. 1,440 ft^3.
To calculate the volume of a triangular prism, you need to multiply the area of the triangular base by the height of the prism.
In this case, the triangular base has a side length of 15 feet and a height of 3 feet (as indicated by the dashed line). To find the area of the triangular base, you can use the formula for the area of a triangle: (base * height) / 2.
Thus, the area of the triangular base is (15 * 3) / 2 = 22.5 square feet.
Next, multiply the area of the base by the height of the prism to find the volume: 22.5 square feet * 16 feet = 360 cubic feet.
Therefore, the volume of the triangular prism is 360 ft3, which rounds to the nearest whole unit.
So, the correct option is A. 360 ft3.