Answer:
A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units^3; therefore, Shannon is correct.
Step-by-step explanation:
Given: Volume of rectangular pyramid= 50 units³
Height= 5 units.
Lets assume the base area of the pyramid be "BA"
We know, volume of pyramid= [tex]\frac{1}{3} \times Base\ area\times height[/tex]
As given, height =5 and volume of pyramid= 50 units.
Subtituting the value in the formula to find base area of Pyramid
⇒ [tex]50= \frac{1}{3} \times BA\times 5[/tex]
Multiplying both side by 3 and dividing both side by 5
⇒ [tex]BA= \frac{50\times 3}{5}[/tex]
∴[tex]BA= 30\ units[/tex]
hence, base area of pyramid is 30 units.
Now, finding the volume of prism.
As given Prism with the same base area and height.
Formula; volume of prism= [tex]base\ area\times height[/tex]
⇒ volume of prism= [tex]30\times 5[/tex]
∴ Volume of prism= 150 unts³
Hence, A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units^3; therefore, Shannon is correct.
