The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its total surface area is 504 cm^2 , find its dimensions. Also, find the volume of the cuboid.

Given: The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. The total surface area of the cuboid = 504 cm 2 . Let the length, breadth and height of cuboid be 6a, 5a and 3a. As we know, the total surface area of the cuboid = 2(l x b \+ b x h \+ h x l) ⇒ 2(6a x 5a \+ 5a x 3a \+ 3a x 6a) = 504 ⇒ 2(30a 2 \+ 15a 2 \+ 18a 2 ) = 504 ⇒ 2 x 63a 2 = 504 ⇒ 126a 2 = 504 ⇒ a 2 = ⇒ a 2 = 4 ⇒ a = ⇒ a = 2 Thus, length of the cuboid = 6a = 6 x 2 cm = 12 cm Breadth of the cuboid = 5a = 5 x 2 cm = 10 cm Height of the cuboid = 3a = 3 x 2 cm = 6 cm As we know that volume of cuboid = l x b x h = 12 x 10 x 6 cm 3 = 720 cm 3 Hence, the dimensions of the cuboid are 12 cm , 10 cm and 6 cm and the volume is 720 cm 3 .

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

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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.

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Find the length of each edge of a cube, if its volume is :
(i) 216 cm³
(ii) 1.728 m³

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The total surface area of a cube is 216 cm². Find its volume.

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Mathematics

The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its total surface area is 504 cm², find its dimensions. Also, find the volume of the cuboid.

Surface Area, Volume, Capacity

Related Questions

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

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.

Find the length of each edge of a cube, if its volume is :
(i) 216 cm³
(ii) 1.728 m³

The total surface area of a cube is 216 cm². Find its volume.

Mathematics

The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its total surface area is 504 cm2, find its dimensions. Also, find the volume of the cuboid.

Surface Area, Volume, Capacity

Related Questions

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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.

Find the length of each edge of a cube, if its volume is :(i) 216 cm3(ii) 1.728 m3

The total surface area of a cube is 216 cm2. Find its volume.

The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its total surface area is 504 cm², find its dimensions. Also, find the volume of the cuboid.

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

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.

Find the length of each edge of a cube, if its volume is :
(i) 216 cm³
(ii) 1.728 m³

The total surface area of a cube is 216 cm². Find its volume.