Quadrilateral pyramid
Calculate the volume of a regular quadrilateral pyramid, which has the size of the base edge a = 12 cm and a height of 11 cm.
Correct answer:
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Dr. Math
To calculate the volume of a regular quadrilateral pyramid, we use the formula:
Here’s the step-by-step solution:
- The base is a square with edge length a = 12 cm .
- The height of the pyramid is h = 11 cm .
The base is a square, so its area is:
Substitute a = 12 cm :
Using the formula for the volume of a pyramid:
Substitute the base area and height:
The volume of the regular quadrilateral pyramid is:
V = 1/3 × Base Area × Height
Here’s the step-by-step solution:
Step 1:
Identify the Given Information- The base is a square with edge length a = 12 cm .
- The height of the pyramid is h = 11 cm .
Step 2:
Calculate the Base AreaThe base is a square, so its area is:
Base Area = a2
Substitute a = 12 cm :
Base Area = 122 = 144 cm2
Step 3:
Apply the Volume FormulaUsing the formula for the volume of a pyramid:
V = 1/3 × Base Area × Height
Substitute the base area and height:
V = 1/3 × 144 × 11
Step 4:
Perform the CalculationV = 1/3 × 144 × 11
V = 1/3 × 1584
V = 528 cm3
Final Answer:
The volume of the regular quadrilateral pyramid is:
528 cm3
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