Question

The are of the floor of a room is 85.5m2. its volume is 983.25m3. find the height of the room.

Answer 1

$\begin{gathered}\begin{gathered}\bf\: Given-\begin{cases} &\sf{Volume_{(room)} = 983.25 \: {m}^{3} } \\ &\sf{Area_{(floor)} = 85.5 \: {m}^{2} } \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To \: Find - \begin{cases} &\sf{Height, \: h_{(room)}}\end{cases}\end{gathered}\end{gathered}$

$\large\underline{\sf{Solution-}}$

Given that,

$\: \: \: \: \: \: \bull \: \: \sf \: \: \: Volume_{(room)} = 983.25 \: {m}^{3}$

$\: \: \: \: \: \: \bull \: \: \sf \: \: \: Area_{(floor)} = 85.5 \: {m}^{2}$

↝ We know that,

$\rm :\longmapsto\:Volume_{(room)} = Area_{(floor)} \times Height$

↝ On substituting the values, we get

$\rm :\longmapsto\:983.25 = 85.5 \times h$

$\rm :\implies\:h \: = \: 11.5 \: m$

$\bf\implies \:Height, \: h \: = \: 11.5 \: m$

Additional Information :-

↝ Cube: 

• A cube has six faces, eight vertices and twelve edges. All the faces of the cube are in square shape and have equal dimensions.

↝ Cuboid: 

• A cuboid has six faces, eight vertices and twelve edges and faces of the cuboid are parallel. But not all the faces of a cuboid are equal in dimensions.

↝ Formula's of Cube :-

• Total Surface Area = 6(side)²

• Curved Surface Area = 4(side)²

• Volume of Cube = (side)³

• Diagonal of a cube = √3(side)

• Perimeter of cube = 12 x side

↝ Formula's of Cuboid

• Total Surface area = 2 (Length x Breadth + breadth x height + Length x height)

• Curved Surface area = 2 height(length + breadth)

• Volume of the cuboid = (length × breadth × height)

• Diagonal of the cuboid =√(l² + b² + h²)

• Perimeter of cuboid = 4 (length + breadth + height)