Chapter 12.9, Problem 17IP

To determine

To find : Which container should they buy.

Answer to Problem 17IP

Cylindrical shape of container.

Explanation of Solution

Given information :

The given information is,

Height ( $h$ ) = $10$ in., Length = $5.5$ and Breadth ( $b$ ) = $5$ in., Height of cylinder ( $h_1$ ) = $9.7$ in. and Diameter of cylinder ( $d$ ) = $6$ in.

So radius ( $r$ ) = $3$ in.

Formula Used:

Surface Area of cuboid open at top = $2h(l+b)+l\times b$

Surface Area of cylinder open at top = $2\pi rh+\pi r^2$

Calculation :

Surface Area of cuboid open at top

  $20(10.5)+5.5\times 5=210+27.5=237.5\text{ in}{\text{.}}^{\text{2}}$

Surface Area of cylinder open at top

  $\begin{array}{l}=2\times 3.14\times 3\times 9.7\times 9\pi \\ =182.748+28.26\\ =211.01\text{ in}{\text{.}}^{\text{2}}\end{array}$

As amount of cardboard required less in cylindrical shape.

So, they buy cylinerical container.