Question

The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same. The volume of pyramid A is___ the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B____ is the volume of pyramid A.

Answer 1

Given:
Pyramid A: Base is rectangle with length of 10 meters and width of 20 meters.
Pyramid B: Base is square with 10 meter sides.
Heights are the same.

Volume of rectangular pyramid = (L * W * H) / 3
Volume of square pyramid = a² * h/3

Let us assume that the height is 10 meters.
V of rectangular pyramid = (10m * 20m * 10m)/3 = 2000/3 = 666.67 m³
V of square pyramid = (10m)² * 10/3 = 100m² * 3.33 = 333.33 m³

The volume of pyramid A is TWICE the volume of pyramid B.

If the height of pyramid B increases to twice the of pyramid A, (from 10m to 20m),

V of square pyramid = (10m)² * (10*2)/3 = 100m² * 20m/3 = 100m² * 6.67m = 666.67 m³

The new volume of pyramid B is EQUAL to the volume of pyramid A.

Answer 2

The volume of pyramid A is twice of pyramid B.

The new volume of pyramid B is equal to the volume of pyramid A.

Explanation:

Given :The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same.

To find : The volume of pyramid A is___ the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B____ is the volume of pyramid A.

Solution :

The volume of a pyramid is the heights of the pyramids are the same.

Let the height of both pyramids be 'h'.

The volume of pyramid is
`V=(1)/(3)bh`

Where, B is base area and h is height of the pyramid.

The volume of Pyramid A is

`V_A=(1)/(3)(10* 20)h`

`V_A=(200)/(3)h` ....(1)

The volume of Pyramid B is

`V_B=(1)/(3)(10* 10)h`

`V_B=(100)/(3)h` ....(2)

We conclude from equations (1) and (2),

`(200)/(3)h=2* (100)/(3)h`

`V_A=2* V_B`

The volume of pyramid A is twice of pyramid B.

Now, the height of pyramid B increased to twice that of pyramid A.

Let the height of pyramid B is 2h and height of pyramid A is h.

The volume of Pyramid A is

`V_A=(1)/(3)(10* 20)h`

`V_A=(200)/(3)h` ....(3)

The volume of Pyramid B is

`V_B=(1)/(3)(10* 10)2h`

`V_B=(200)/(3)h` .....(4)

We conclude from equations (3) and (4),

`V_A=V_B`

The new volume of pyramid B is equal to the volume of pyramid A.