Question

Select the correct answer from each drop-down menu. 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

Step-by-step explanation:

The formula of a volume of a pyramid:

$V=\dfrac{1}{3}BH$

B - base area

H - height

H - height of pyramids

Pyramid A:

$B=(10)(2)=200\ m^2$

$V_A=\dfrac{1}{3}(200)H=\dfrac{200}{3}H\ m^3$

Pyramid B:

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

$V_B=\dfraC{1}{3}(100)H=\dfrac{100}{3}H\ m^3$

$V_A>V_B\\\\V_A=2V_B$

The volume of the pyramid A is twice as large as the volume of the pyramid B.

The new height of pyramid B: 2H

The new volume:

$V_{B'}=\dfrac{1}{3}(100)(2H)=\dfrac{200}{3}H\ m^3$

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