The length, breadth and height of a cuboid (rectangular solid) are 4 : 3 : 2.
(i) If its surface area is 2548 cm², find its volume.
(ii) If its volume is 3000 m³, find its surface area.

Question

The length, breadth and height of a cuboid (rectangular solid) are 4 : 3 : 2. (i) If its surface area is 2548 cm², find its volume. (ii) If its volume is 3000 m³, find its surface area.

KnowledgeBoat · Accepted Answer

(i) It is given that the length, breadth and height of a cuboid are 4 : 3 : 2. The surface area = 2,548 cm². Let the length, breadth and height of a cuboid be 4a, 3a and 2a. As we know that surface area of cuboid = 2(l x b \+ b x h \+ h x l) ⇒ 2(4a x 3a \+ 3a x 2a \+ 2a x 4a) = 2,548 ⇒ 2(12a² \+ 6a² \+ 8a²) = 2,548 ⇒ 2 x 26a² = 2,548 ⇒ 52a² = 2,548 ⇒ a² = ⇒ a² = 49 ⇒ a = ⇒ a = 7 cm Thus, length of the cuboid = 4a = 4 x 7 cm = 28 cm Breadth of the cuboid = 3a = 3 x 7 cm = 21 cm Height of the cuboid = 2a = 2 x 7 cm = 14 cm Volume of the cube = l x b x h = 28 x 21 x 14 cm³ = 8,232 cm³ Hence, the volume of the cube is 8,232 cm³. (ii) The volume of the cube = 3,000 m³ As we know that volume of cube = l x b x h ⇒ 4a x 3a x 2a = 3,000 ⇒ 24a³ = 3,000 ⇒ a³ = ⇒ a³ = 125 ⇒ a = ⇒ a = 5 m Thus, length of the cuboid = 4a = 4 x 5 m = 20 m Breadth of the cuboid = 3a = 3 x 5 m = 15 m Height of the cuboid = 2a = 2 x 5 m = 10 m The surface area of cuboid = 2(l x b \+ b x h \+ h x l) = 2(20 x 15 \+ 15 x 10 \+ 10 x 20) m² = 2(300 \+ 150 \+ 200) cm² = 2 x 650 cm² = 1,300 m² Hence, the surface area of the cuboid is 1,300 m².

Mathematics

The length, breadth and height of a cuboid (rectangular solid) are 4 : 3 : 2.
(i) If its surface area is 2548 cm², find its volume.
(ii) If its volume is 3000 m³, find its surface area.

Surface Area, Volume, Capacity

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Mathematics

The length, breadth and height of a cuboid (rectangular solid) are 4 : 3 : 2.(i) If its surface area is 2548 cm2, find its volume.(ii) If its volume is 3000 m3, find its surface area.

Surface Area, Volume, Capacity

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(ii) If its volume is 3000 m³, find its surface area.

The ratio between the lengths of the edges of two cubes are in the ratio 3 : 2. Find the ratio between their :
(i) total surface area
(ii) volume.

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