Respuesta :
Answer:
Rs 2464
Step-by-step 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;
[tex]Length = 2 * Breadth\\L = 2 * B[/tex]---> (1) and [tex]Breadth = 2 * Height\\B = 2 * H[/tex]----> (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.
[tex]Volume of the room = L * B * H[from given data, and eq. {1} and eq. {2}][/tex]
[tex]512 = 2B * 2H * H[/tex]
[tex]512 = 2 * 2H * 2H * H[/tex]
[tex]512 = 4H * 2H^{2}[/tex]
[tex]512 = 8H^{3}[/tex]
[tex]H^{3} = \frac{512}{8}[/tex]
[tex]H^{3} = 64[/tex]
[tex]H = \sqrt[3]{64}[/tex]
[tex]H = 4 m[/tex]
[tex]Now, put\\ value\\ of \\H \\in \\eq. {2}[/tex]
[tex]B = 2 * H[/tex]
[tex]B = 2 * 4[/tex]
[tex]B = 8 m[/tex]
[tex]\\[/tex]Now, put value of B in eq. {1}
[tex]L = 2 * B[/tex]
[tex]L = 2 * 8[/tex]
[tex]L = 16 m[/tex]
Now, we have to find out area of the room, so we use formula of total surface area of cuboid.
[tex]Area of the room = 2*L*B + 2*L*H + 2*H*B[/tex]
[tex]Area of the room = 2 * 16 * 8 + 2 * 16 * 4 + 2 * 4 * 8[/tex]
[tex]Area of the room = 32 * 8 + 32 * 4 + 8 * 8[/tex]
[tex]Area of the room = 256 + 128 + 64[/tex]
[tex]Area of the room = 384 + 64[/tex]
[tex]Area of the room = 448 m^{2}[/tex]
Now, to find out room wall plastering cost
[tex]Room wall plastering cost = Area of the room * cost of plastering per ^{2}[/tex]
[tex]Room wall plastering cost = 448 * 5.50[/tex]
[tex]Room wall plastering cost = Rs 2464[/tex]
[tex]ence, the room wall plastering cost is Rs 2464.[/tex]
