The length, breadth and height of a closed box are respectively 2m, 1.5m and 0.8m. Find the total area of canvas required to cover it-up. Find also the cost of canvas if 1sq m of canvas costs Rs. 30.
A rectangular box without lid is to be made by thin sheet of metal. Find the area of the sheet required if the box is 8m long, 4m wide and 2m deep.
Help me!
surface area = 2(2)(1.5) + 2(2)(.8) + 2(1.5)(.8)
= 11.6 m^2
@ 30 per m^2
cost = 30(11.6) = 348
#2
SA = 1(8)(4) + 2(8)(2) + 2(4)(2)
= ...
To find the total area of canvas required to cover a closed box, we need to find the area of each side of the box individually and then add them together.
In this case, the box has length (L) = 2m, breadth (B) = 1.5m, and height (H) = 0.8m.
To find the total area, we need to consider 5 sides of the box: the top (L x B), bottom (L x B), front (L x H), back (L x H), and sides (B x H) of the box.
1. Top and Bottom: The dimensions of the top and bottom are L x B. So, the area of both would be 2 x (L x B) = 2 x (2m x 1.5m) = 6m².
2. Front and Back: The dimensions of the front and back are L x H. So, the area of both would be 2 x (L x H) = 2 x (2m x 0.8m) = 3.2m².
3. Sides: The dimensions of the sides are B x H. So, the area of both sides would be 2 x (B x H) = 2 x (1.5m x 0.8m) = 2.4m².
Therefore, the total area of canvas required to cover the box would be: (Top + Bottom) + (Front + Back) + (Sides)
= 6m² + 3.2m² + 2.4m²
= 11.6m².
Now, to find the cost of canvas, we multiply the total area by the cost per square meter.
Cost of canvas = Total area x Cost per square meter
= 11.6m² x Rs. 30/m²
= Rs. 348.
So, the cost of canvas required to cover the box would be Rs. 348.
For the second part, to find the area of the sheet required to make a rectangular box without a lid, we need to find the surface area of the box.
Given dimensions: length (L) = 8m, width (B) = 4m, and depth (D) = 2m.
The surface area of the box is given by the formula: 2(LB + BD + LD).
Substituting the values, the surface area of the box would be:
= 2(8m x 4m + 4m x 2m + 8m x 2m)
= 2(32m² + 8m² + 16m²)
= 2(56m²)
= 112m².
Therefore, the area of the sheet required to make the box would be 112m².