Respuesta :
Answer:
a) [tex]S(s) = 14s^2[/tex]
b) [tex]V(s) = 3s^3[/tex]
c) [tex]S(s) = \dfrac{14V(s)}{3s}[/tex]
d) 56 square meter
Step-by-step explanation:
We are given the following in the question:
A closed box with a square bottom is three times high as it is wide.
Let s be the side of square and h be the height.
[tex]h = 3s[/tex]
a) Surface area of box
[tex]2(lb + bh + hl)[/tex]
where l is the length, b is the breadth and h is the height.
Putting values:
[tex]S = 2(s^2 + sh +sh)\\S = 2(s^2 + 3s^2 + 3s^2)\\S(s) = 14s^2[/tex]
b) Volume of box
[tex]l\times b \times h[/tex]
where l is the length, b is the breadth and h is the height.
Putting values:
[tex]V = s\times s\times h\\V= s\times s\times 3s\\V(s) = 3s^3[/tex]
c) Surface area in terms of volume
[tex]S(s) = 14s^2 = \dfrac{14V(s)}{3s}[/tex]
d) Surface area
Volume = 24 m³
[tex]V(s) = 24\\3s^3 = 24\\s^3 = 3\\s = 2[/tex]
[tex]S(2) = 14(2)^2 = 56\text{ square meter}[/tex]
