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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 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.21 metres15 metres16 metres15 metres Q 2: The length, width and height of a cuboid are 20 metres, 15 metres and 10 metres respectively. Find the total surface area of the cuboid.1400 square metres1600 square metres1500 square metres1300 square metres Q 3: The length and height of a cuboid are 8 metres and 4 metres respectively. Find the width if the total surface area of the cuboid is given by 208 square metres.9 metres11 metres6 metres4 metres Q 4: 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.8 metres5 metres11 metres6 metres Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!