Question

The Length Of A Room is two time its breadth and breadth is two time its height If The volume of room is 512m2 what is the cost of plastering its wall at rs 5.50 per m2​

Answer 1

Rs 2464

Explanation:

Given:

• The length of a room is 2 times its breadth and breadth is 2 times its height. The volume of the room is 512 cubic metre.

To find:

• The cost of plastering it's wall at Rs 5.50 per square metre.

Solution : A/C to given data;

`Length = 2 * Breadth\\L = 2 * B`---> (1) and
`Breadth = 2 * Height\\B = 2 * H`----> (2)

A/C to given data let, structure of room is cuboidal.

Now, we have to find out the height of the room, so we use formula of volume of the cuboid.

`Volume of the room = L * B * H[from given data, and eq. {1} and eq. {2}]`

`512 = 2B * 2H * H`

`512 = 2 * 2H * 2H * H`

`512 = 4H * 2H^(2)`

`512 = 8H^(3)`

`H^(3) = (512)/(8)`

`H^(3) = 64`

`H = \sqrt[3]{64}`

`H = 4 m`

`Now, put\\ value\\ of \\H \\in \\eq. {2}`

`B = 2 * H`

`B = 2 * 4`

`B = 8 m`

`\\`Now, put value of B in eq. {1}

`L = 2 * B`

`L = 2 * 8`

`L = 16 m`

Now, we have to find out area of the room, so we use formula of total surface area of cuboid.

`Area of the room = 2*L*B + 2*L*H + 2*H*B`

`Area of the room = 2 * 16 * 8 + 2 * 16 * 4 + 2 * 4 * 8`

`Area of the room = 32 * 8 + 32 * 4 + 8 * 8`

`Area of the room = 256 + 128 + 64`

`Area of the room = 384 + 64`

`Area of the room = 448 m^(2)`

Now, to find out room wall plastering cost

`Room wall plastering cost = Area of the room * cost of plastering per ^(2)`

`Room wall plastering cost = 448 * 5.50`

`Room wall plastering cost = Rs 2464`

`ence, the room wall plastering cost is Rs 2464.`