Question

two square pyramids have the same volume.the base edge of one is half that of other.how many times the height of the second pyramid is the height of the first ?please answer its urgent​

Answer 1

The height of the second pyramid is 4 times the height of the first.

Step-by-step explanation:

Let’s assume  

The volume of the first pyramid and the second pyramid be denoted as “V1” and “V2” respectively.

The base edge of first pyramid be “a1”  and the base edge of the second pyramid be “a2”.

The height of the first pyramid be “h1” and the height of the second pyramid be “h2”.

It is given the base edge of one is half that of other so, a2 = a1/2

The formula for the volume of a square pyramid is given as,

V = 1/3 * [base area] * [height] = 1/3 * a² * h  

We are given that the volume of both the square pyramids is equal.

Therefore, based on the above formula, we get

V1 = V2

⇒ 1/3 * a1² * h1 = 1/3 * a2² * h2

⇒ a1² * h1 = (a1/2)² * h2

⇒ a1² * h1 = a1²/4 * h2

⇒ h2 = 4*h1

Thus, the height of the second pyramid is four times the height of the first pyramid.

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Answer 2

Height of the second pyramid is 4 times the height of the first pyramid.

Step-by-step explanation:

Consider the provided information.

There are two square pyramids.

The volume of pyramid is: $\frac{1}{2}(\text{Base area})(\text{Height})$

Let the volume, base edge and height of first pyramid is V₁, A₁ and H₁ respectively.

Let the volume, base edge and height of Second pyramid is V₂, A₂ and H₂ respectively.

It is given that Volume of both pyramids are same.

Now substitute the respective values:

$\frac{1}{2}(A_1)^2(H_1)=\frac{1}{2}(A_2)^2(H_2)$

The base edge of one is half that of other. Let the base edge of second pyramid is half the first pyramid.

$\frac{1}{2}(A_1)^2(H_1)=\frac{1}{2}(\frac{A_1}{2})^2(H_2)$

$H_1=\frac{1}{4}(H_2)$

$H_2=4H_1$

Height of the second pyramid is 4 times the height of the first pyramid.

#Learn more

A regular square pyramid is 3m height and perimeter of its base is 16m. Find volume of pyramid

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