How to find the volume of a pyramid - SAT Math
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A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.
A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.
If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.
Since the base is a square, the area of the base is 3 x 3 = 9.
Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.
If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.
Since the base is a square, the area of the base is 3 x 3 = 9.
Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.
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The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?
The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?
Volume of a pyramid is
Thus:
Area of the base is 
.
Therefore, each side is 
.
Volume of a pyramid is
Thus:
Area of the base is
Therefore, each side is
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Find the volume of the pyramid shown below:
Find the volume of the pyramid shown below:
The formula for the area of a pyramid is 
. In this case, the length is 
, the width is 
, and the height is 
.
and 
.
The formula for the area of a pyramid is
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Figure not drawn to scale
In the pyramid above, the base is a square. The distance between points C and D is 6 inches and the length of side b is 5 inches. What is the volume of this pyramid?
Figure not drawn to scale
In the pyramid above, the base is a square. The distance between points C and D is 6 inches and the length of side b is 5 inches. What is the volume of this pyramid?
To find the volume of a pyramid, you need to use the equation below:
To find the height (shown by the yellow line), we can draw a right triangle using the yellow line, blue line and side b (5 inches). Because the hypotenuse is 5 inches, using the common Pythagorean 3-4-5 triple. The blue line is 3 inches and the yellow line (height) is 4 inches. Also, to find side a, we can use the blue line (3 inches) and half of the red line (3 inches) and the Pythagorean Theorum.
Because the base is a square, the area of the base is equal to the square of side a:
Now we plug in these values to find the volume:
To find the volume of a pyramid, you need to use the equation below:
To find the height (shown by the yellow line), we can draw a right triangle using the yellow line, blue line and side b (5 inches). Because the hypotenuse is 5 inches, using the common Pythagorean 3-4-5 triple. The blue line is 3 inches and the yellow line (height) is 4 inches. Also, to find side a, we can use the blue line (3 inches) and half of the red line (3 inches) and the Pythagorean Theorum.
Because the base is a square, the area of the base is equal to the square of side a:
Now we plug in these values to find the volume:
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Calculate the volume of the rectangular pyramid with height 
, base width 
, and base length 
Calculate the volume of the rectangular pyramid with height
The volume 
of a rectangular pyramid with height 
, base width 
, and base length 
is given by
.
For this pyramid, 
, 
, and 
To calculate its volume, substitute the values for 
, 
, and 
into the formula:
Therefore, the volume of the given rectangular pyramid is 
The volume
For this pyramid,
Therefore, the volume of the given rectangular pyramid is
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