Question

tana fills the prism shown (3 1/4 and 4 inch) with 110 1/2 in squared of liquid what is the height of the prism

Answer 1

(X)(3.25)(4)= 110.5
4
(x)(3.25)= 27.625
3.25
x = 8.5
(8.5)(3.25)(4)= 110.5

Answer 2

Answer:

$h=8\frac{1}{2}\text{ inch}$

Step-by-step explanation:

Let h represent height of prism.

We have been given that Tana fills the prism with base lengths $3\frac{1}{4}$ inch and $4$ inch with a $110\frac{1}{2}\text{ inch}^3$.

We know that volume of prism is area of base times height, so we can set an equation as:

$\text{Volume of prism}=\text{Base length}\times\text{Base width}\times \text{Height of prism}$

$110\frac{1}{2}\text{ inch}^3=3\frac{1}{4}\text{ inch}\times 4\text{ inch}\times h$

$\frac{221}{2}\text{ inch}^3=\frac{13}{4}\text{ inch}\times 4\text{ inch}\times h$

$\frac{221}{2}\text{ inch}^3=13\text{ inch}^2\times h$

$\frac{221}{2*13\text{ inch}^2}\text{ inch}^3=\frac{13\text{ inch}^2\times h}{13\text{ inch}^2}$

$\frac{221}{26}\text{ inch}=h$

$8\frac{13}{26}\text{ inch}=h$

$8\frac{1}{2}\text{ inch}=h$

Therefore, the height of the prism is $8\frac{1}{2}\text{ inch}$.