A manufacturer made a container that looked like the Washington Monument to fill with raisins, as shown. Find the volume of the container
the sides on the bottom are 2 inches for the base and the height is 7 inches
To find the volume of the container shaped like the Washington Monument, we need to calculate the volume of a triangular prism. First, we determine the area of the base triangle and then multiply it by the height.
The base of the triangular prism is in the shape of a triangle, with sides measuring 2 inches. The formula to find the area of a triangle is A = (base x height) / 2.
Since the base triangle is an equilateral triangle, all three sides are equal. Therefore, the height of the triangle can be calculated using the Pythagorean theorem. Considering one of the equal sides as the base, we have:
a² + b² = c²,
2² + b² = 2b² = c²,
b² = 4 - b²,
2b² = 4,
b² = 2,
b = √2.
Thus, the height (b) of the base triangle is √2 inches.
To calculate the area of the base triangle, we substitute the values into the formula:
A = (base x height) / 2
A = (2 x √2) / 2
A = √2 square inches.
Now, we can multiply the area of the base triangle by the height of the triangular prism to find the volume:
Volume = Area of base x Height
Volume = √2 square inches x 7 inches
Volume = 7√2 cubic inches.
Therefore, the volume of the container is 7√2 cubic inches.