Question

A rectangular pyramid has a height of 5 units and a volume of 50 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?

Answer 1

Answer:

A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.

Step-by-step explanation:

Answer 2

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= $\frac{1}{3} \times Base\ area\times height$

As given, height =5 and volume of pyramid= 50 units.

Subtituting the value in the formula to find base area of Pyramid

⇒ $50= \frac{1}{3} \times BA\times 5$

Multiplying both side by 3 and dividing both side by 5

⇒ $BA= \frac{50\times 3}{5}$

∴$BA= 30\ units$

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= $base\ area\times height$

⇒ volume of prism=  $30\times 5$

∴ 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.