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### Grade 7 - Mathematics9.48 Surface Area of Cuboid - I

 Example: The length, width and height of a cuboid are 10 metres, 8 metres and 7 metres respectively. Find the lateral surface area of the cuboid. Solution: Given that, l = 10 metres, b = 8 metres and h = 7 metres Equation for lateral surface area = 2h (l+b). Substituting the values of l, b and h we get, = 2 * 7 (10 + 8) = 14 * 18 = 252 square metres. Example: The width and height of a cuboid are 6 metres and 4 metres respectively. Find the length if the lateral surface area of the cuboid is given by 300 square metres. Solution: Given that, b = 6 metres and h = 4 metres Equation for lateral surface area = 2h (l+b). Substituting the values of b and h we get, = 2 * 4 (l + 6) Therefore 8 * (l + 6) = 300 i.e 8l + 48 = 300 i.e 8l = 300 - 48 = 252 i.e l = 252 / 8 Therefore l = 31.5 Hence length of the cuboid is 31.5 metres. Directions: Read the above example carefully and answer the following questions: The length of a cuboid is 5 more than the width and 3 less than the height. If the lateral surface area is given by 256 square metres, then find its length, width and height. The length, width and height of a cuboid is given by x, 3x and 5x. Then find the lateral surface area. Also find the area when x = 10 metres.
 Q 1: The length, width and height of a cuboid are 17 metres, 9 metres and 4 metres respectively. Find the lateral surface area of the cuboid.108 square metre208 square metre408 square metre308 square metre Q 2: The width and height of a cuboid are 10 metres and 6 metres respectively. Find the length of the cuboid if the lateral surface area is given by 288 square metres.12 metres14 metres19 metres18 metres Q 3: The length and height of a cuboid are 8 metres and 2 metres respectively. Find the width if the lateral surface area of the cuboid is given by 56 square metres.4 metres1 metre6 metres2 metres Q 4: The width and height of a cuboid are 10 metres and 6 metres respectively. Find the length if the lateral surface area of the cuboid is given by 264 square metres.16 metres20 metres18 metres12 metres Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!