Two similar pyramids have lateral areas f 20 square feet and 45 sqaure feet. The vloume of the smaller pyramid is 8 cubic feet. Find the volume of the larger pyramid.
33ft^3
27ft^3
18ft^3
12ft^3
Can some explain how to solve this.
the areas scale as the square of the ratio
the volumes scale as the cube of the ratio
so, volumes scale as the 3/2 power of the area ratio
So thar larger pyramid's volume is
8*(40/25)^(3/2) = 8 * (9/4)^(3/2) = 8 * 27/8 = 27
Thank you, I think I undertsand this. I will give it a try.
Steve is correct
Sure! Allow me, the Clown Bot, to explain it to you with a touch of humor.
To find the volume of the larger pyramid, we can use a magical formula. But be careful! It only works when you feed it the right numbers, otherwise, it'll just give you a bunch of nonsense.
First, let's define some variables:
Let's call the volume of the smaller pyramid V₁ and the volume of the larger pyramid V₂.
We can also call the lateral area of the smaller pyramid A₁ and the lateral area of the larger pyramid A₂.
Now, the magical formula we're going to use is:
V₂ = V₁ × (A₂ / A₁)
It's like a fraction, but with letters instead of numbers. Fancy, huh?
So, in this case, we know that the lateral area of the smaller pyramid is 20 square feet and the lateral area of the larger pyramid is 45 square feet. We also know that the volume of the smaller pyramid is 8 cubic feet.
Plugging in the numbers into the formula, we get:
V₂ = 8 × (45 / 20)
Now, to do some math. *Calculating... calculating...*
Ah, the answer is 18 cubic feet! So the volume of the larger pyramid is 18 ft³. Ta-da!
Hope that made you smile while learning. Don't hesitate to ask if you have more questions!
To solve this problem, we need to use the formulas for the lateral area and volume of a pyramid.
The formula for the lateral area of a pyramid is given by:
Lateral Area = (1/2) * Perimeter of Base * Slant Height
The formula for the volume of a pyramid is given by:
Volume = (1/3) * Base Area * Height
Let's assume that the lateral area of the smaller pyramid is 20 square feet, and the lateral area of the larger pyramid is 45 square feet.
First, we need to find the ratio between the lateral areas of the two pyramids.
Ratio of lateral areas = Lateral Area of larger pyramid / Lateral Area of smaller pyramid
Ratio of lateral areas = 45 sq ft / 20 sq ft
Next, we need to find the ratio between the volumes of the two pyramids.
Since the ratio of the lateral areas is the square of the ratio of the corresponding linear dimensions, we can find the ratio of the volumes by taking the square root of the ratio of lateral areas.
Ratio of volumes = Square root of (Ratio of lateral areas)
Now, we have the ratio of volumes, and we know the volume of the smaller pyramid is 8 cubic feet. We can use this information to find the volume of the larger pyramid.
Let's calculate the ratio of volumes using the given lateral areas:
Ratio of lateral areas = 45 sq ft / 20 sq ft = 2.25
Ratio of volumes = Square root of (2.25) = 1.5
Now, to find the volume of the larger pyramid, we can use the formula for the volume of a pyramid:
Volume of larger pyramid = Volume of smaller pyramid * Ratio of volumes
Volume of larger pyramid = 8 cubic ft * 1.5
Volume of larger pyramid = 12 cubic ft
Therefore, the volume of the larger pyramid is 12 cubic ft.