Question

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

prism is 2 square units. The area of the base of the red prism is one third that
of the blue prism. Which statement is true?

a)The height of the red prism is one-third the height of the blue prism.
b)The height of the red prism is the same as the height of the blue prism.
c)The height of the red prism is six times the height of the blue prism.
d)The height of the red prism is three times the height of the blue prism.

Answer 1

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

Explanation:

i) the volume of a rectangular prism is given by area of base
`*` height.

ii) volume of the blue prism is = (base of blue prism)
`*` (height of blue prism)

iii) volume of red prism is = (base of red prism)
`*` ( height of the red prism)

=
`(1)/(3)`
`*` ( base of blue prism)
`\height`
`*` ( height of red prism)

iv) it is also given that

volume of blue prism = volume of red prism

⇒ (base of blue prism)
`*` (height of blue prism) = (base of red prism)
`*` (height of red prism)

⇒(base of blue prism)
`*` (height of blue prism) =
`(1)/(3)`
`*` ( base of blue prism)
`*` (height of red prism)

⇒ (height of blue prism) =
`(1)/(3)`
`*` (height of red prism)

∴ height of red prism = 3
`*` height of blue prism

Therefore the correct option is

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