Grade 7 - Mathematics 9.49 Surface Area of Cuboid - II
The length, breadth and height of a cuboid are 16 metres, 14 metres and 10 metres respectively. Find the total surface area of the cuboid.
l = 16 metres, b = 14 metres and h = 10 metres. Equation for total surface area = 2 (l*b + b*h + h*l)
= 2 (16*14 + 14*10 + 16*10)
= 2 (224 + 140 + 160)
= 2 (524)
= 1048 square metres.
The width and height of a cuboid are 13 metres and 12 metres respectively. Find the length if the lateral surface area of the cuboid is given by 1600 square metres.
Let 'x' be the length.
b = 13 metres and h = 12 metres Equation for total surface area = 2 (l*b + b*h + h*l)
Substituting the values of b and h we get,
1600 = 2 (x*13 + 13*12 + 12*x)
i.e 1600 = 2 (13x + 156 + 12x)
i.e 1600 = 2 (25x + 156) = 50x + 312
i.e 50x = 1600-312 = 1288.
Therefore x = 1288/50 = 25.76.
Hence length of the cuboid is 25.76 metres.
Directions: Read the above example carefully and answer the following questions:
The length of a cuboid is 2 more than the width and 3 less than the height. If the ltotal surface area is given by 1126 square metres, then find its length, width and height.
The length, width and height of a cuboid is given by 3x, 2x and 5x. Then find the total surface area. Also find the area when x = 2 metres.