What is the volume of a right triangular pyramid whose base is 5 meters on each side and whose altitude is 4 meters?
The volume of a pyramid can be calculated using the formula:
V = (1/3) * base area * height
In this case, the base is a right triangle, so the base area can be calculated using the formula for the area of a triangle:
A = (1/2) * base * height
Substituting the values given:
A = (1/2) * 5m * 4m
= 10m²
Now, we can calculate the volume using the formula for a pyramid:
V = (1/3) * 10m² * 4m
= (1/3) * 40m³
= 13.33m³
Therefore, the volume of the right triangular pyramid is 13.33 cubic meters.
To find the volume of a right triangular pyramid, you can use the formula:
Volume = (1/3) * base area * height
In this case, the base of the pyramid is a right-angled triangle with sides of 5 meters each, and the altitude is given as 4 meters.
Step 1: Calculate the area of the triangular base:
The area of a right-angled triangle can be calculated using the formula:
Area = (1/2) * base * height
In this case, the base and height are both 5 meters, so the area of the base is:
Area = (1/2) * 5 * 5
Area = (1/2) * 25
Area = 12.5 square meters
Step 2: Calculate the volume of the pyramid:
Using the formula:
Volume = (1/3) * base area * height
Substituting the values we found:
Volume = (1/3) * 12.5 * 4
Volume = (1/3) * 50
Volume = 16.67 cubic meters
Therefore, the volume of the right triangular pyramid with a base of 5 meters on each side and an altitude of 4 meters is approximately 16.67 cubic meters.