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 twice that of pyramid A, the new volume of pyramid B is the volume of pyramid B.If the height of pyramid B increases to the volume of pyramid A.

Answer 1

The volume of rectangle pyramid can be calculated using formula:

$V_{pyramid}=\dfrac{1}{3}\cdot \text{length}\cdot \text{width}\cdot \text{height}.$

1. If the base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters, then

$V_{A}=\dfrac{1}{3}\cdot 10\cdot 20\cdot H_A=\dfrac{200}{3}H_A.$

2. If the base of pyramid B is a square with 10-meter sides, then

$V_{B}=\dfrac{1}{3}\cdot 10\cdot 10\cdot H_B=\dfrac{100}{3}H_B.$

3. If heights $H_A,\ H_B$ are the same, you can see that

$V_{A}=2V_{B}.$

Answer 1: twice (2 times)

If $H_B=2H_A,$ then

$V_{B}=\dfrac{100}{3}H_B=\dfrac{100}{3}\cdot 2H_A=\dfrac{200}{3}H_A=V_{A}.$

Answer 2: the same

Answer 2

Answer:

The volume of pyramid A is twice of pyramid B and if the height of pyramid B increased to twice that of pyramid A, the new volume of pyramid B is the equal to the volume of pyramid A.

Step-by-step explanation:

Given information:

Pyramid A: Rectangular base of 10×20.

Pyramid B: Square base of 10×10.

It is given that

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

Let the height of both pyramids be h.

$V=\frac{1}{3}Bh$

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

The volume of Pyramid A is

$V_A=\frac{1}{3}(10\times 20)h$

$V_A=\frac{200}{3}h$

The volume of Pyramid B is

$V_B=\frac{1}{3}(10\times 10)h$

$V_B=\frac{100}{3}h$

We conclude that,

$\frac{200}{3}h=2\times \frac{100}{3}h$

$V_A=2\times V_B$

It means 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.

$V_A=\frac{1}{3}(10\times 20)h$

$V_A=\frac{200}{3}h$

The volume of Pyramid B is

$V_B=\frac{1}{3}(10\times 10)2h$

$V_B=\frac{200}{3}h$

$V_B=V_A$

Therefore the volume of pyramid A is twice of pyramid B and if the height of pyramid B increased to twice that of pyramid A, the new volume of pyramid B is the equal to the volume of pyramid A.