Question

The volume of the triangular block is 4 cubic inches. What is the approximate length of y? Round to the nearest 10th of an inch.

Answer 1

2.8 in

Explanation:

The volume (V) of the prism is calculated as

V = Ah ( A is the area of the triangular end and h is the length )

A =
`(1)/(2)` × x × x =
`(1)/(2)` x² , thus

V =
`(1)/(2)` x² × x = 4 , that is

`(1)/(2)` x³ = 4 ( multiply both sides by 2 )

x³ = 8 ( take the cube root of both sides )

x =
`\sqrt[3]{8}` = 2

Using Pythagoras' identity on the right triangle with hypotenuse y, then

y² = x² + x² = 2² + 2² = 4 + 4 = 8 ( take the square root of both sides )

y =
`√(8)` ≈ 2.8 in ( to the nearest tenth )