Respuesta :
Given:
Volume of room = 1296 cubic feet
One side of the square floor of the room = 12 ft
Radistor is ⅓ of the height of the room.
Let's find the area covered by the mirror.
Here, the room has the shape of a square prism.
To find the height of the room, apply the formula:
[tex]V=a^2\ast h[/tex]Where:
V = 1296 cubic feet
a = 12 ft
Let's solve for h:
[tex]\begin{gathered} 1296=12^2\ast h \\ \\ 1296=144\ast h \\ \\ \text{Divide both sides by 144:} \\ \frac{1296}{144}=\frac{144\ast h}{144} \\ \\ 9=h \\ \\ h=9\text{ ft} \end{gathered}[/tex]The height of the room is 9 feet.
Given that the radiator is ⅓ of the height of the room.
We have:
[tex]\begin{gathered} \frac{1}{3}\ast h \\ \\ =\frac{1}{3}\ast9 \\ \\ =3\text{ ft} \end{gathered}[/tex]This means the height of the radiator is 3 ft
Let's find the area covered by the mirror.
Apply the area of a rectangle.
Since the radiator covers the entire length of the room, the length the radiator covers is 12 ft
The height of the radiator is 3ft
[tex]\begin{gathered} A=3\ast12 \\ \\ A=36\text{ square fe}et \end{gathered}[/tex]Therefore, the area covered by the G mirror is 36 square feet
ANSWER:
36 square feet
