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### Grade 7 - Mathematics9.49 Surface Area of Cuboid - II

 Example: 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. Solution: Given that, 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. Example: 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. Solution: Let 'x' be the length. Given that, 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.
 Q 1: The length and height of a cuboid are 12 metres and 10 metres respectively. Find the width if the total surface area of the cuboid is given by 724 square metres.5 metres8 metres6 metres11 metres Q 2: The length and width and height of a cuboid are 16 metres, 14 metres and 12 metres respectively. Find the height if the total surface area of the cuboid is given by 1168 square metres.12 metres21 metres11 metres7 metres Q 3: The width and height of a cuboid are 14 metres and 13 metres respectively. Find the length if the total surface area of the cuboid is given by 1174 square metres.15 metres21 metres16 metres15 metres Q 4: The length, width and height of a cuboid are 18 metres, 16 metres and 15 metres respectively. Find the total surface area of the cuboid.1695 square metres1596 square metres1965 square metres2596 square metres Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!