A cuboid has a total surface area of 80 m² and the lateral surface area of 50 m²; the area of its base is :
30 m²
60 m²
15 m²
10 m²

Question

A cuboid has a total surface area of 80 m 2^ and the lateral surface area of 50 m^2; the area of its base is : 1. 30 m^2  2. 60 m 2^ 3. 15 m^2  4. 10 m^2

KnowledgeBoat · Accepted Answer

The total surface area of the cuboid = 80 m² The lateral surface area of the cuboid = 50 m² As we know, the total surface area of the cuboid = 2(l x b \+ b x h \+ h x l) ⇒ 80 = 2(l x b \+ b x h \+ h x l) ⇒ 80 = 2(l x b) \+ 2(b x h) \+ 2(h x l) ..............(1) The lateral surface area of the cuboid = 2(l \+ b)h = 2(l x h \+ b x h) ⇒ 50 = 2(l x h) \+ 2(b x h) ..............(2) And, area of base = l x b Putting the value of 2(l x h) \+ 2(b x h) from equation (2) in equation (1), we get ⇒ 80 = 2(l x b) \+ 50 ⇒ 2(l x b) = 80 \- 50 ⇒ 2(l x b) = 30 ⇒ l x b = ⇒ l x b = 15 m² Hence, option 3 is the correct option.

Mathematics

A cuboid has a total surface area of 80 m² and the lateral surface area of 50 m²; the area of its base is :
30 m²
60 m²
15 m²
10 m²

Surface Area, Volume, Capacity

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