Question

22. The volume of a cuboid is 140cm. The areas of its any two surfaces are 28cmn- and 20 cm. The sum of the lengths of all edges of the cuboid is- (1) 140 cm (2) 160 cm (3) 100 cm (4) 64 cm​

Answer 1

Answer:

option b 160 is the answer ok

Answer 2

Correct Question

22. The volume of a cuboid is 140cm³. The areas of any two of its surfaces are 28cm² and 20 cm². The sum of the lengths of all edges of the cuboid is-

(1) 140 cm

(2) 160 cm

(3) 100 cm

(4) 64 cm​

Answer

The sum of all edges is (4) 64 cm.

Given

• The volume of a cuboid is 140cm³
• The areas of any two surfaces are 28cm²

To Find

The sum of the lengths of all edges of the cuboid

Solution

Let the three dimensions of a cuboid be l, b, and h.

According to the question,

lbh = 140 cm³                                                                         [1]

let the surfaces be lb and lh

According to the problem

lb = 28 cm²                                                                            [2]                                            

lh = 20 cm²                                                                            [3]

From equations [1] and [2] we get,

28h = 140

or, h = 140/28

or, h = 5 cm                                                                            [4]

Similarly, from equations [1] and [3] we get,

40b = 140

b = 140/20

or, b = 7 cm

From equations [3] and [4] we get

5l = 20

or, l = 20/5

or, l = 4 cm

A cuboid has 12 edges, i.e 4 edges of length, breadth, and height each.

Hence, sum of all edges = 4(l + b + h) = 4(7 + 5 + 4) = 4 X 16 cm

= 64 cm

Hence, the sum of all edges is (4) 64 cm.

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