Lateral Surface Area of a Cuboid
Lateral Surface Area of a Cuboid
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If out of the six faces of a cuboid, we only find the sum of the areas of four faces leaving the bottom and top faces. This sum is called the Lateral surface area of the cuboid. Consider a cuboid of the length l, breadth b, and height h Lateral surface area of the cuboid = Area of face ABGF + Area of face BCHG + Area of face EFGH + Area of face ADEF = 2(b x h) + 2(l x h) = 2(l + b) x h = Perimeter of base x height Note: Base of a cuboid is a rectangle. |
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Illustration: A cubical box has each edge 10cm and another cuboidal box is 12.5cm long, 10cm wide, and 8cm high. Which box has the greater lateral surface area and by how much?
Solution: Let the lateral surface areas of the cubical and cuboidal boxes be Area1 and Area2 respectively. Then, Area 1 = = 4 x 10 x 10 =
Area 2 = 2 (Length + Breadth) x Height = 2 (12.5 + 10) x 8 =
Area of cube is more than the area of cuboid = 400 - 360 =
Illustration: Find the area of the four walls of a room whose length is 6 m, breadth 5 m and height 4 m.Also find the cost of white-washing the walls, if the rate of whitewashing is Rs 5 per square metre.
Solution: Given: l = 6 m, b = 5 m, and h = 4 m
Area of the walls = 2h(l + b)
Cost of white washing of 1 square metre = Rs. 5
So, Cost of white washing the walls = Rs(5 X 88) = Rs 440
A cuboid has total surface area of 40 sq m and its lateral surface area is 26 sq m. Find the area of its base. | |||
| Right Option : B | |||
| View Explanation | |||
A wooden box (open at the top) of thickness 0.5 cm, length 21 cm, width 11 cm and height 6 cm is painted on the inside. The expenses of paintings are Rs. 70. What is the rate of painting per square centimeter? | |||
| Right Option : C | |||
| View Explanation | |||
The floor of a rectangular hall has a perimeter 250m. If the cost of painting the four walls at the rate of Rs.10 per sq m is Rs 15000, find the height of the wall. | |||
| Right Option : A | |||
| View Explanation | |||
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