Question

A cuboid has a total surface area of 96 cm². The
sum of the squares of its length, breadth, and height
(in cm) is 48. Find its height (in cm).
(a) 3
(b) 4.
(C) 5
(d) 6​

Answer 1

Answer:

let length = l

breadth = b

height = h

now , total surface area = 2(lb+bh+hl) = 96

and

l² +b² +h² = 48

multiply by 2

2l² +2b² +2h² = 96..(2)

now , subtract 2 from 1

2l² +2b² +2h² - (2(lb+bh+hl)) = 96-96 =0

l² +b² - 2lb + b² +h²-2bh + h²+l²-2lh =0

(l-b)² + (b-h)² +(h-l)² = 0

(l-b)² = 0 (b-h)² = 0 , (h-l)²= 0

i.e

l=b , b= h , l = h

thus l=b=h

l² +b² +h² = 48

h² +h²+h² = 48

3h² = 48

h² = 16

h = 4 cm

Step-by-step explanation:

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Answer 2

Answer:

Answer: To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surfaceThe surface area of a cuboid can be calculated by adding together the areas of the six faces. The opposite faces of a cuboid are the same sized rectangles, so find the total area of the three different faces, then double to find the total surface area.Volume of a cuboid = (length × breadth × height) cubic units. = (l × b × h) cubic units. Let us look at the given cuboid. We find that volume of the given cuboid with length 5 cm, breadth 3 cm and height 2 cm is 30 cu cm.

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