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.

Accepted Solution

Step-by-step explanation:The formula of a volume of a pyramid:[tex]V=\dfrac{1}{3}BH[/tex]B - base areaH - heightH - height of pyramidsPyramid A:[tex]B=(10)(2)=200\ m^2[/tex][tex]V_A=\dfrac{1}{3}(200)H=\dfrac{200}{3}H\ m^3[/tex]Pyramid B:[tex]B=10^2=100\ m^2[/tex][tex]V_B=\dfraC{1}{3}(100)H=\dfrac{100}{3}H\ m^3[/tex][tex]V_A>V_B\\\\V_A=2V_B[/tex]The volume of the pyramid A is twice as large as the volume of the pyramid B.The new height of pyramid B: 2HThe new volume:[tex]V_{B'}=\dfrac{1}{3}(100)(2H)=\dfrac{200}{3}H\ m^3[/tex]The volume of the pyramid A is equal to the volume of the pyramid B.