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Maths-

General

Easy

Question

Find the Total surface area if the given dimensions are 6 cm,4cm, and 5 cm.

164 cm²
120 cm²
148 cm²
134 cm²

hint Hint:

Hint:- We have given three different dimensions ,
Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
where
l → length of the cuboid
b → breadth of the cuboid
h → height of the cuboid

The correct answer is: 148 cm²

We will calculate the total surface area of a cuboid by using the following formula:

$text T.S.A. of a cuboid end text equals 2 cross times left square bracket 1 b plus b h plus h l right square bracket$

The dimensions of the given cuboid:
Length, l = 4 cm
Breadth, b = 5 cm
Height, h = 6 cm
By using the above formula of the total surface area of the cuboid, we get
The total surface area of the given cuboid is,
= $2 cross times left square bracket left parenthesis l b right parenthesis plus left parenthesis b h right parenthesis plus left parenthesis h l right parenthesis right square bracket$
= $2 cross times left square bracket left parenthesis 4 cross times 5 right parenthesis plus left parenthesis 5 cross times 6 right parenthesis plus left parenthesis 6 cross times 4 right parenthesis right square bracket$
= $2 cross times left square bracket 20 plus left parenthesis 30 right parenthesis plus left parenthesis 24 right parenthesis right square bracket$
= $2 cross times 74$
= 148 cm²
Thus, the total surface area of a cuboid of dimensions 6 cm, 4 cm & 5 cm is 148 cm².
The correct option is C)148 cm².
Note:- In some examples it may be given the surface area and any two dimensions , then we have to adjust the formula such a that we will be able to find out the required value . For eg- If area , length and breadth is given the formula for height becomes
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator text Area end text over denominator 2 end fraction minus l b equals b h plus h l end cell row cell fraction numerator text Area end text over denominator 2 end fraction minus l b equals h left parenthesis b plus l right parenthesis end cell row cell h equals fraction numerator text Area end text over denominator 2 left parenthesis b plus l right parenthesis end fraction minus fraction numerator l b over denominator left parenthesis b plus l right parenthesis end fraction end cell end table$

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