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Answer:
Step-by-step explanation:
Given question is incomplete; here is the complete 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.
Since, volume of pyramid = [tex]\frac{1}{3}(\text{Area of the base})(\text{Height})[/tex]
Volume of the pyramid A = [tex]\frac{1}{3}(\text{length}\times \text{Width})(\text{height})[/tex]
= [tex]\frac{1}{3}(10\times 20)(h)[/tex]
= [tex]\frac{200h}{3}[/tex]
Volume of pyramid B = [tex]\frac{1}{3}(10)^2(h)[/tex]
= [tex]\frac{100h}{3}[/tex]
Ratio of the volumes of the pyramids = [tex]\frac{\text{Volume of pyramid A}}{\text{Volume of pyramid B}}[/tex]
= [tex]\frac{\frac{200h}{3}}{\frac{100h}{3} }[/tex]
= 2
Therefore, volume of pyramid A is TWICE the volume of pyramid B.
If If height of the pyramid B increases twice of pyramid A,
Then the volume of pyramid B = [tex]\frac{1}{3}(100)(2h)[/tex]
= [tex]\frac{200h}{3}[/tex]
Ratio of volumes of pyramid B and pyramid A = [tex]\frac{\text{Volume of pyramid B}}{\text{Volume of pyramid A}}[/tex]
= [tex]\frac{\frac{200h}{3}}{\frac{200h}{3}}[/tex]
= 1
Therefore, new volume of pyramid B is EQUAL to the volume of pyramid A.
