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 volume.

Given: The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. Total surface area of cuboid = 504 cm 2 . Let the length, breadth and height of cuboid be 6a, 5a and 3a. As we know total surface area of 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 cuboid = 6a = 6 x 2 cm = 12 cm Breadth of cuboid = 5a = 5 x 2 cm = 10 cm Height of 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 volume of cuboid is 720 cm 3 .

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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 volume.

Surface Area, Volume, Capacity

Related Questions

A cuboid is 8 m long, 12 m broad and 3.5 m high. Find its
(i) total surface area
(ii) lateral surface area

How many bricks will be required for constructing a wall which is 16 m long, 3 m high and 22.5 cm thick, if each brick measures 25 cm x 11.25 cm x 6 cm ?

The external dimensions of an open wooden box are 65 cm, 34 cm and 25 cm. If the box is made up of wood 2 cm thick, find the capacity of the box and the volume of wood used to make it.

The curved surface area and the volume of a toy, cylindrical in shape, are 132 cm² and 462 cm³ respectively. Find its diameter and its length.

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 volume.

Surface Area, Volume, Capacity

Related Questions

A cuboid is 8 m long, 12 m broad and 3.5 m high. Find its(i) total surface area(ii) lateral surface area

How many bricks will be required for constructing a wall which is 16 m long, 3 m high and 22.5 cm thick, if each brick measures 25 cm x 11.25 cm x 6 cm ?

The external dimensions of an open wooden box are 65 cm, 34 cm and 25 cm. If the box is made up of wood 2 cm thick, find the capacity of the box and the volume of wood used to make it.

The curved surface area and the volume of a toy, cylindrical in shape, are 132 cm2 and 462 cm3 respectively. Find its diameter and its length.

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 volume.

A cuboid is 8 m long, 12 m broad and 3.5 m high. Find its
(i) total surface area
(ii) lateral surface area

The curved surface area and the volume of a toy, cylindrical in shape, are 132 cm² and 462 cm³ respectively. Find its diameter and its length.