Question

The volume of an iron rod of height equal to 1 metre is 1386 cubic centimetre. Find the diameter of this iron rod.

Answer 1

Hint: Assume a variable r which will represent the radius of the given iron rod. In surface area and volume, we have a formula which is used to calculate the volume of a cylinder. The volume of a cylinder with radius r and height h is given by the formula $V=\pi {{r}^{2}}h$. Since the iron rod can also be considered as a cylinder, we can use the above formula to solve this question.

Complete step-by-step answer:
Before proceeding with the question, we must know the formula that will be required to solve this question.

In surface area and volume, the volume of a cylinder of radius r and height h is given by the formula,

$V=\pi {{r}^{2}}h$ . . . . . . . . . . (1)

In this question, we are given that the volume of an iron rod of height equal to 1 metre is 1386 cubic centimetre. We are required to find the diameter of this iron rod.

Let us consider r to be the radius of this iron rod. Since volume is given in cubic centimetre, we have to convert the height in centimetres as well. The height in centimetres will be equal to 100 cm. Substituting V, r, h, $\pi $ is formula (1), we get,

$\begin{align}

  & 1386=\dfrac{22}{7}{{r}^{2}}\left( 100 \right) \\

 & \Rightarrow {{r}^{2}}=\dfrac{1386\times 7}{22\times 100} \\

 & \Rightarrow {{r}^{2}}=\dfrac{63\times 7}{100} \\

 & \Rightarrow {{r}^{2}}=\dfrac{7\times 7\times 9}{10\times 10} \\

 & \Rightarrow r=\sqrt{\dfrac{7\times 7\times 3\times 3}{10\times 10}} \\

 & \Rightarrow r=\dfrac{7\times 3}{10} \\

 & \Rightarrow r=2.1cm \\

\end{align}$

Since the diameter is twice the radius, the diameter is equal to 4.2 cm.

Hence, the answer is 4.2 cm.

Note: There is a possibility that one may note convert the height from metre to centimetres. But since volume is given in cubic centimetres, we have to convert the height into centimetres as well. Also, there is a possibility that one may write the radius i.e. 2.1 cm as the answer instead of the diameter i.e. 4.2 cm.