Question

The area of the base of a rectangular prism can be represented by B, and the height is represented by h.

a. Write an equation that represents the volume of the prism.
b. If the area of the base is doubled, write an equation that represents the volume of the prism.
c. If the height of the prism is doubled, write an equation that represents the volume of the prism.
d. Compare the volume in parts (b) and (c). What do you notice about the volumes?
e. Write an expression for the volume of the prism if both the height and the area of the base are doubled.

Answer 1

a) V=B×h

b) V₁=2B×h

c) V₂=B×2h

d) V₁=V₂

e) V₃=4Bh

Explanation:

a) The volume of a rectangular prism is given by the multiplication of hte area of the base B and the height h, so the equation is: V=B×h

b) If the area of the base is doubled the equation is: V₁=2B×h

c) If the height of the prism is doubled the equation is: V₂=B×2h

d)We can check that V₁=2B×h and V₂=B×2h are the same. (V₁=V₂)

e) If both the height and the area of the base are doubled, the equation is given by:

V₃=2B×2h=4Bh