Question

how does the total surface area of a box change if each dimenction is tripled​

Answer 1

Answer:

let length =L

width=B

height=H

surface area of box=2{LB+BH+HL}

(a) all dimensions are double

so ,

new length =2L

width=2B

height =2H

now surface area=2{(2L)(2B)+(2B)(2H)+(2H)(2L)}

=4 x 2{LB+BH+HL}

compare we see 4times surface of box

(b) if all dimensions triples

then

surface area of box=2{(3L)(3B)+(3B)(3H)+(3H)(3L)}

=9 x 2 {LB+BH+HL}

we see surface area of box now, 9 times

yes " i find if dimensions raised n times

surface area of box then n^2 times

by above observation .

Step-by-step explanation:

Answer 2

GIVEN-:

How does the total surface area of a box change if each dimenction is tripled?

Needed Answer-:

Total surface area,T.S.A of a box=6×side²

Let Side Be "a"

so,

T.S.A [OLD]= 6a²

If side=3a

T.S.A [NEW]⬇️⬇️(SLIDE DOWN TO VIEW ANSWER)

$- > {6(3{a}^{2}}) \\ - > 6 \times 9 {a}^{2} \\ - > 54 {a}^{2}$

Answer-:

54a²

@Answered by Its Spidey