a square pyramid has the base length of 10 cm. The slant height of the pyramid is 13 cm what is the volume?
+23254 The volume of a pyramid can be found by: V = (1/3)x(Area of the base)x(height)
Since its base is a square with side length of 10, the area of the base is 10x10 = 100.
To find the height: A right triangle is formed from the top point to the center of the base and then out to the middle of a side and then back to the top point.
The distance from the center of the base to the middle of a side is 5.
The distance from the middle of a side to the top point is 13 (and this is the hypotenuse of the right triangle).
Using the Pythagorean Theorem: a2 + b2 = c2 ---> a2 + 52 = 132
Solving this for a: a = 12 ---> the height = 12.
So: V = (1/3)(100)(12) = ...
+23254 The volume of a pyramid can be found by: V = (1/3)x(Area of the base)x(height)
Since its base is a square with side length of 10, the area of the base is 10x10 = 100.
To find the height: A right triangle is formed from the top point to the center of the base and then out to the middle of a side and then back to the top point.
The distance from the center of the base to the middle of a side is 5.
The distance from the middle of a side to the top point is 13 (and this is the hypotenuse of the right triangle).
Using the Pythagorean Theorem: a2 + b2 = c2 ---> a2 + 52 = 132
Solving this for a: a = 12 ---> the height = 12.
So: V = (1/3)(100)(12) = ...
