Chapter 22, Problem 1A

To determine

To find the weight of the $92.4$ centimeter piece of steel nearest to half kilogram.

Answer to Problem 1A

  $54\frac{1}{2}$ kilogram.

Explanation of Solution

Given information:

A sheet if steel $280$ centimeter long weighs $165$ kilograms. A $92.4$ centimeter long sheet is sheared from the sheet.

Calculation:

As per the given information a sheet if steel $280$ centimeter long weighs $165$ kilograms. A $92.4$ centimeter long sheet is sheared from the sheet.

As per the definition of proportion ration of length and weight of whole sheet will be proportional to ratio of length and weight of sheared sheet.

i.e. $\frac{\text{Weight of whole sheet}}{\text{Length of whole sheet}}=\frac{\text{Weight of sheared sheet}}{\text{Length sheared sheet}}$

  $\begin{array}{l}\Rightarrow \frac{165\text{ kg}}{280\text{ cm}}=\frac{\text{Weight of the sheared sheet}}{92.4\text{}\text{cm}}\\ \text{Apply cross multiplication,}\\ \Rightarrow \text{Weight of the sheared sheet }\times 280\text{ cm}=165\text{ kg}\times \text{92}\text{.4 cm}\\ \Rightarrow \text{Weight of the sheared sheet}=\frac{165\times 92.4}{280}\text{ kg}\\ \Rightarrow \text{Weight of the sheared sheet}=54.45\text{ kg}\\ \end{array}$

Hence, weight of the sheared sheet nearest to half Kilogram will be $54\frac{1}{2}$ kilogram.