The base of a right triangular prism is a right isosceles triangle whose equal sides measure 25 cm. each. The volume of the prism is 7.5 cubic meters. Find the height of the prism.
Area of base = (1/2)(.25)(.25 sin 60)
= .0271 m^2
.0271 * h = 7.5
h = 277
To find the height of the prism, we can use the formula for the volume of a right triangular prism.
The formula for the volume of a right triangular prism is given by:
Volume = (base area) x height
Step 1: Find the base area of the prism.
Since the base of the right triangular prism is an isosceles triangle, we can find the area of the base using the formula for the area of a triangle.
Base area = (1/2) x base x height
In this case, the base of the triangle is equal to one of the equal sides, which measures 25 cm. The height of the triangle is also equal to one of the equal sides, so it is also 25 cm.
Base area = (1/2) x 25 cm x 25 cm = 312.5 square cm
Step 2: Convert the base area to cubic meters.
Since the volume of the prism is given in cubic meters, we need to convert the base area from square centimeters to square meters.
1 square meter = 10,000 square centimeters
Base area in square meters = 312.5 square cm / 10,000 = 0.03125 square meters
Step 3: Substitute the values into the volume formula to solve for height.
Volume = 7.5 cubic meters
Base area = 0.03125 square meters
7.5 cubic meters = (0.03125 square meters) x height
Divide both sides of the equation by 0.03125:
height = 7.5 cubic meters / 0.03125 square meters
height ≈ 240 meters
Therefore, the height of the prism is approximately 240 meters.