The length, the breadth and the height of a cuboid are in the ratio 5 : 3 : 2. If its volume is 240 cm³, find its dimensions. Also, find the total surface area of the cuboid.
Surface Area, Volume, Capacity
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Question

The length, the breadth and the height of a cuboid are in the ratio 5 : 3 : 2. If its volume is 240 cm^3 , find its dimensions. Also, find the total surface area of the cuboid.

KnowledgeBoat · Accepted Answer

Given: The length, breadth and height of a cuboid are in the ratio 5 : 3 : 2. The volume of the cuboid = 240 cm³. Let the length, breadth and height of cuboid be 5a, 3a and 2a. As we know that the volume of the cuboid = l x b x h ⇒ 5a x 3a x 2a = 240 cm³ ⇒ 30a³ = 240 ⇒ a³ = ⇒ a³ = 8 ⇒ a = ⇒ a = 2 cm Thus, the length of the cuboid = 5a = 5 x 2 = 10 cm Breadth of the cuboid = 3a = 3 x 2 = 6 cm Height of the cuboid = 2a = 2 x 2 = 4 cm As we know, the total surface area of the cuboid = 2(l x b \+ b x h \+ h x l) = 2(10 x 6 \+ 6 x 4 \+ 4 x 10) cm² = 2(60 \+ 24 \+ 40) cm² = 2 x 124 cm² = 248 cm² Hence, the dimensions of the cuboid are 10 cm , 6 cm and 4 cm and the total surface area is 248 cm².

Mathematics

The length, the breadth and the height of a cuboid are in the ratio 5 : 3 : 2. If its volume is 240 cm³, find its dimensions. Also, find the total surface area of the cuboid.

Surface Area, Volume, Capacity

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Mathematics

The length, the breadth and the height of a cuboid are in the ratio 5 : 3 : 2. If its volume is 240 cm3, find its dimensions. Also, find the total surface area of the cuboid.

Surface Area, Volume, Capacity

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