Question

the perimeter of the base of an artifact shaped like a rectangular prism is 16 inches. The length of the base is 3 times the width of the base. The artifact is 2 1/2 feet tall. What is the volume of the artifact in cubic inches?

Answer 1

The volume of the artifact is $360 \ in^3$

Explanation:

It is given that the perimeter of the artifact is $16 \ in$

Let w be the width of the base.

Let l be the length of the base.

Since, it is given that, "The length of the base is 3 times the width of the base".

Thus, we have,

$l=3w$ and $w=w$

Substituting these values in the perimeter formula, we get,

$P=2(l+w)$

$16=2(3w+w)$

$16=2(4w)$

$8=4w$

$2=w$

Thus, the width of the base is $2 \ in$

The length of the base is $l=3(2)=6 \ in$

Also, the height of the artifact is $2\frac{1}{2} =\frac{5}{2} ft$

To convert feet into inches, we have,

$1 \ feet =12\ inches$

$\frac{5}{2}\times 12=30 \ in$

Thus, the height of the artifact is $30\ i n$

Volume of the artifact = $lwh$

                                    $=(6)(2)(30)$

                                    $=360 \ in^3$

Thus, the volume of the artifact is $360 \ in^3$

learn more:

(1) What is the volume of a rectangular prism with the dimensions: base 5/8 cm, height 2/3 cm, and length 3/4 cm?

brainly.in/question/7636759

(2) Find the volume of rectangular prism whose width is 2cm height of 3cm and lenght of 4 cm

brainly.in/question/8846344

Answer 2

Answer:

Step-by-step explanation:

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