The base of a right pyramid is a rectangle of length 80 cm and width 60 cm. Each slant edge of the pyramid is 230 cm. Calculate the volume of the pyramid.
Attempt to make a 3-D sketch.
The centre of the pyramid will be the intersection of the two diagonals of the base
and they bisect each other.
let d be that diagonal
d^2 = 80^2 +60^2
d = 100
Now draw a right-angled triangle with base 50 , height = h, and hypotenuse = 230
h^2 + 50^2 = 230^2
find h
volume of pyramid = (1/3)(area of base * h)
How did you got base 50 and hy :230
To calculate the volume of a pyramid, we can use the formula:
Volume = (1/3) * base area * height
First, we need to find the height of the pyramid. We can do this by using the Pythagorean theorem.
We have a right triangle formed by the height, the slant edge, and half the length of the rectangle base. Using the Pythagorean theorem, we get:
height^2 + (60/2)^2 = 230^2
Simplifying the equation:
height^2 + 30^2 = 230^2
height^2 + 900 = 52900
height^2 = 52900 - 900
height^2 = 52000
Taking the square root of both sides:
height = √52000
height ≈ 227.92 cm
Now that we have the height, we can calculate the volume using the formula:
Volume = (1/3) * base area * height
The base area of the rectangle is the length multiplied by the width:
Base area = 80 cm * 60 cm
Base area = 4800 cm^2
Volume = (1/3) * 4800 cm^2 * 227.92 cm
Volume ≈ 369,984 cm^3
Therefore, the volume of the pyramid is approximately 369,984 cubic centimeters.
To calculate the volume of the pyramid, we can use the formula:
Volume = (1/3) * Base Area * Height
Considering the base is a rectangle, the base area can be found by multiplying its length and width:
Base Area = Length * Width
The slant edge length can be considered as the height of the pyramid.
Let's calculate the volume step by step:
1. Calculate the base area:
Base Area = 80 cm * 60 cm = 4800 cm²
2. Use the height (slant edge length) to calculate the volume:
Volume = (1/3) * Base Area * Height
Volume = (1/3) * 4800 cm² * 230 cm
3. Simplify the equation:
Volume = 1600 cm² * 230 cm
Volume = 368,000 cm³
Therefore, the volume of the right pyramid is 368,000 cm³.