Question

Two rectangular prisms have the same volume. The area of the base of the blue

Answer 1

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 $\times$ height.

ii) volume of the blue prism is = (base of blue prism) $\times$ (height of blue prism)

iii) volume of red prism is = (base of red prism) $\times$ ( height of the red prism)

               = $\frac{1}{3}$ $\times$ ( base of blue prism) $\height$$\times$  ( height of red prism)

iv) it is also given that

   volume of blue prism = volume of red prism

   ⇒    (base of blue prism) $\times$ (height of blue prism) = (base of red prism)$\times$ (height of red prism)

⇒(base of blue prism) $\times$ (height of blue prism) = $\frac{1}{3}$ $\times$ ( base of blue prism)$\times$ (height of red prism)

⇒ (height of blue prism) = $\frac{1}{3}$ $\times$  (height of red prism)

∴ height of red prism = 3 $\times$ height of blue prism

Therefore the correct option is

d) the height of red prism is three times the height of the blue prism.