Question

the length breadth and height of a cuboid are increased by 30% find the percentage increase in the total surface area​

Answer 1

Answer:

The percentage increase in the total surface area​ will be 69%

Step-by-step explanation:

we know that the Total surface Area of a cuboid is given as,

TSA = 2(LB + BH + LH)

where,

L = length

B = breadth

H = height

let the initial length breadth and height of the cuboid are 10, 10, and 10

=> TSA = 2(100 + 100 + 100 )

=> TSA = 600

Now given that the length breadth and height of the cuboid are increased by 30%

=> 10 + (30/100)x10 = 13

=> New length breadth and height of the cuboid are 13, 13, 13

=> New TSA = 2(13x13 + 13x13 + 13x13)

=> New TSA = 1014

Hence increase in TSA = 1014 - 600 = 414

=> % increase in TSA = 414/600  x 100 = 69%

Hence percentage increase in the total surface area​ will be 69%

Answer 2

Answer:

The percentage increase in the total surface area​ = 69%

Step-by-step explanation:

Formula:-

Surface area of cuboid

Surface area = 2(lb + bh + lh)

l - length

b - breadth

h - height

It is given that, the length breadth and height of a cuboid are increased by 30%

l ⇒ 130/100 * l = 1.3l

b ⇒ 1.3b

h = 1.3h

To find the surface area after increasing the dimensions

Surface area = 2(lb + bh + lh)

=2[1.3l*1.3b + 1.3b*1.3h + 1.3l*1.3h]

= 2[1.69lb + 1.69bh + 1.69lh]

= 2*1.69(lb + bh + lh))

To find the percentage of increase of surface area

Intitial surface area =  2(lb + bh + lh)

New surface area = 2*1.69(lb + bh + lh))

Percentage of increase

= [2*1.69(lb + bh + lh)) -  2(lb + bh + lh)]/[2(lb + bh + lh)]] *100

= 0.69 * 100 = 69%

The percentage increase in the total surface area​ = 69%