Answer:
d) the height of red prism is three times the height of the blue prism.
Step-by-step explanation:
i) the volume of a rectangular prism is given by area of base [tex]\times[/tex] height.
ii) volume of the blue prism is = (base of blue prism) [tex]\times[/tex] (height of blue prism)
iii) volume of red prism is = (base of red prism) [tex]\times[/tex] ( height of the red prism)
= [tex]\frac{1}{3}[/tex] [tex]\times[/tex] ( base of blue prism) [tex]\height[/tex][tex]\times[/tex] ( height of red prism)
iv) it is also given that
volume of blue prism = volume of red prism
⇒ (base of blue prism) [tex]\times[/tex] (height of blue prism) = (base of red prism)[tex]\times[/tex] (height of red prism)
⇒(base of blue prism) [tex]\times[/tex] (height of blue prism) = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] ( base of blue prism)[tex]\times[/tex] (height of red prism)
⇒ (height of blue prism) = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] (height of red prism)
∴ height of red prism = 3 [tex]\times[/tex] height of blue prism
Therefore the correct option is
d) the height of red prism is three times the height of the blue prism.
