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

Answer:

Part 1) The volume of pyramid A is two times the volume of pyramid B

Part 2) The new volume of pyramid B is equal to the volume of pyramid A

Step-by-step explanation:

we know that

The volume of a pyramid is equal to

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

where

B is the area of the base of pyramid

h is the height of the pyramid

Part 1

The heights of the pyramids are the same

Find the volume of pyramid A

Find the area of the base B

$B=10*20=200\ m^{2}$

substitute

$VA=\frac{1}{3}(200)h$

$VA=\frac{200}{3}h\ m^{3}$

Find the volume of pyramid B

Find the area of the base B

$B=10^{2}=100\ m^{2}$

substitute

$VB=\frac{1}{3}(100)h$

$VB=\frac{100}{3}h\ m^{3}$

Compare the volumes

$VA=2VB$

The volume of pyramid A is two times the volume of pyramid B

Part 2)

If the height of pyramid B increases to twice that of pyramid A

we have that

$VA=\frac{200}{3}h\ m^{3}$

Find the new volume of pyramid B

we have

$B=100\ m^{2}$

$h=2h\ m$

substitute

$VB=\frac{1}{3}(100)(2h)$

$VB=\frac{200}{3}h\ m^{3}$

Compare the volumes

$VA=VB$

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

Answer 2

Answer:

The volume of pyramid A is  twice 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  equal to  the volume of pyramid A.

Step-by-step explanation:

Correct for plato :)