Question

A boiler room has the shape of a rectangular prism. The area of the floor of the room is 112 square feet. The length of the room is 2 feet more than twice the width. The height is 1 foot greater than the width. What is the volume of the room in cubic feet? Do not include units in your answer.

Answer 1

Answer:

The volume of the room is 42336.

Step-by-step explanation:

Given,

Area of the floor = $112\ ft^2$

Let the width of the room be x.

Since the length of the room is 2 feet more than twice the width.

$\therefore\ length=2x+2$

Since the room is rectangular, so we use the formula of area of rectangle.

$Area = length\times width$

On substituting the values, we get;

$(2x+2)\times2=112\\\\4x+4=112\\\\4x=112-4\\\\4x=108\\\\x=\frac{108}{4}=27$

Width = 27

$Length = 2x+2=2\times27+2=54+2=56$

The height is 1 foot greater than the width.

$\therefore Heigth=27+1=28$

Now,

Length = 56    Width = 27     Heigth = 28

And we know volume of a rectangular prism is length times width times height.

$Volume =length\times width\times\ height.$

$Volume = 56\times27\times28= 42336\ ft^3$

Thus the volume of the room is 42336.

Answer 2

Answer:

896

Step-by-step explanation:

112=(2w+2)W

W=7,-8 cant be negitive so 7

L=(7)2+(7)=16

H=7+1=8

V=7*16*8

V=896