Question

The total surface area of all six sides of the rectangular box is equal to 80 square inches. What is the volume of the rectangular box in cubic inches?
a.40
b.48
c.12
d.30

Answer 1

Hint: If $l,b,h$ are the length, breadth and height of a rectangular box respectively, then its total surface area if given by $S = 2\left( {lb + bh + hl} \right)$.

Complete step-by-step answer:
Let $l,b,h$ be the length, breadth and height of the given rectangular box respectively.
$
   \Rightarrow l = 4'' \\
   \Rightarrow b = x'' \\
   \Rightarrow h = 4'' \\
 $
It is given that the total surface area of the box= $80inc{h^2}$
$ \Rightarrow $ $2(lb + bh + lh) = 80$
$ \Rightarrow $$2(4x + 4x + 16) = 80$
$ \Rightarrow $$16x + 32 = 80$
$ \Rightarrow $$x + 2 = 5$
$ \Rightarrow $$x = 3''$
Hence the volume of the box which is given by V is
$V = l \times b \times h$
$ \Rightarrow $\[V = 4 \times 3 \times 4\]
$ \Rightarrow $\[V = 48inc{h^3}\] : The volume of the given box.

Note: Try to remember these formulas. The curved surface area or partial surface area of a rectangular box is given by
$CSA = 2(l + b) \times h$
The total surface area of a rectangular box is given by
$TSA = 2(lb + bh + lh)$
Volume of a rectangular box is given by
$V = l \times b \times h$