Question

It requires a 1322 cm long ribbon to tie a cubical gift pack. Find the length of the gift pack if a 50 cm ribbon is used in the flower knot.

Answer 1

Hint: Here, we will find the length of the ribbon to tie a gift pack only by subtracting the length of the flower knot from the length of the ribbon. Then by using the length of the ribbon we will find the surface area of a cube. We will use the surface area of a cube to find the length of a cubical gift pack.

Formula Used:
Total Surface Area of a cube is given by the formula $6{a^2}$ where $a$ is the side of the cube.

Complete step-by-step answer:
It is given that the total length of the ribbon is 1322 cm and the length of the flower knot only is 50 cm.
Now, we will find the length of a ribbon to tie a cubical gift pack only by subtracting the length of the flower knot only from the total length of the ribbon.
Length of a Ribbon to tie a Cubical gift pack only $ = $ Total length of the ribbon $ - $ length of the flower knot
Substituting the values in the above equation, we get
$ \Rightarrow $ Length of a Ribbon to tie a Cubical gift pack only $ = 1322 - 50$
Subtracting the terms, we get
$ \Rightarrow $ Length of a Ribbon to tie a Cubical gift pack only $ = 1272{\text{cm}}$
Thus, we will find the Surface area of a cube by dividing the length of a ribbon to tie a Cubical gift pack only by 2.
Surface area of a cube $ = $ Length of a Ribbon to tie a Cubical gift pack only $ \div 2$
Substituting the value in the above equation, we get
$ \Rightarrow $ Surface area of a cube $ = \dfrac{{1272}}{2}$
Dividing the terms, we get
$ \Rightarrow $ Surface area of a cube $ = 636{\text{c}}{{\text{m}}^2}$
We know that the total surface area of a cube is $6{a^2}$.
Now, by using the formula, we get
$ \Rightarrow 6{a^2} = 636$
Dividing both sides by 6, we get
$ \Rightarrow {a^2} = \dfrac{{636}}{6}$
$ \Rightarrow {a^2} = 106{\text{c}}{{\text{m}}^2}$
By taking square root on both the sides, we get
$ \Rightarrow a = \sqrt {106} {\text{cm}}$
$ \Rightarrow a = 10.295{\text{cm}}$
$ \Rightarrow a \simeq 10.3{\text{cm}}$
Therefore, the length of a cubical gift pack is $10.3{\text{cm}}$ .


Note: Here, we need to keep in mind that we have to find the length of the cubical gift pack and not the length of the ribbon. So, we can make a mistake if we find the length of the ribbon and end up getting the wrong answer. We know that a cube is a three-dimensional figure and it is bounded by the square on all the sides. The total surface area of a cube is the total area covered by a cube.