2 Answers

Anuith · Answer 1 · 2018-08-27T21:34:24+0000

Answer:

$h=8(1)/(2)\text{ inch}$

Explanation:

Let h represent height of prism.

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

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

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

$110(1)/(2)\text{ inch}^3=3(1)/(4)\text{ inch}* 4\text{ inch}* h$

$(221)/(2)\text{ inch}^3=(13)/(4)\text{ inch}* 4\text{ inch}* h$

$(221)/(2)\text{ inch}^3=13\text{ inch}^2* h$

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

$(221)/(26)\text{ inch}=h$

$8(13)/(26)\text{ inch}=h$

$8(1)/(2)\text{ inch}=h$

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

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