Chapter 14, Problem 61A

To determine

To find the weight of aluminum for $15$ castings.

Answer to Problem 61A

$5265$ pound.

Given information:

A casting is given with dimensions in millimeter as below.

  

Calculation:

Here we observe that the casting is made by putting a smaller cube on top of a larger cube. So, volume of casting will be equal to summation of volume of both cube.

As we know that volume of a cube is given by -

$V=s^3$

Here, side length of the smaller cube is $8.2$ inch. i.e. $s=8.2$ inch.

So, volume of the smaller cube will be -

$\begin{array}{l}V=s^3\\ $ \Rightarrow V={(8.2)}^3\text{cubic inch }\text{{Put }s=8.2\text{ inch}}$\Rightarrow V=551.368\text{cubic inch}\\ \Rightarrow V=551.37\text{cubic inch {Rounding off to two decimal place}}\end{array}$

Similarly, side length of the larger cube is $14.5$ inch. i.e. $s=14.5$ inch.

So, volume of the smaller cube will be -

$\begin{array}{l}V=s^3\\ $ \Rightarrow V={(14.5)}^3\text{cubic inch }\text{{Put }s=14.5\text{ inch}}$\Rightarrow V=3048.625\text{cubic inch}\\ \Rightarrow V=3048.62\text{cubic inch {Rounding off to two decimal place}}\end{array}$

Total volume of casting $=551.37+3048.62\text{ cubic inch}=3600\text{ cubic inch}$

Now, weight of aluminum is $0.0975$ pound per cubic inch.

So, weight of aluminum for $3600$ cubic inch $=$

$0.0975\times 3600=351$ pound.

This is the weight of aluminum for one casting.

Therefore, weight of aluminum for $15$ castings $=351\times 15=5265\text{ pound}$.

Explanation of Solution

Given information:

A casting is given with dimensions in millimeter as below.

  

Calculation:

Here we observe that the casting is made by putting a smaller cube on top of a larger cube. So, volume of casting will be equal to summation of volume of both cube.

As we know that volume of a cube is given by -

$V=s^3$

Here, side length of the smaller cube is $8.2$ inch. i.e. $s=8.2$ inch.

So, volume of the smaller cube will be -

$\begin{array}{l}V=s^3\\ $ \Rightarrow V={(8.2)}^3\text{cubic inch }\text{{Put }s=8.2\text{ inch}}$\Rightarrow V=551.368\text{cubic inch}\\ \Rightarrow V=551.37\text{cubic inch {Rounding off to two decimal place}}\end{array}$

Similarly, side length of the larger cube is $14.5$ inch. i.e. $s=14.5$ inch.

So, volume of the smaller cube will be -

$\begin{array}{l}V=s^3\\ $ \Rightarrow V={(14.5)}^3\text{cubic inch }\text{{Put }s=14.5\text{ inch}}$\Rightarrow V=3048.625\text{cubic inch}\\ \Rightarrow V=3048.62\text{cubic inch {Rounding off to two decimal place}}\end{array}$

Total volume of casting $=551.37+3048.62\text{ cubic inch}=3600\text{ cubic inch}$

Now, weight of aluminum is $0.0975$ pound per cubic inch.

So, weight of aluminum for $3600$ cubic inch $=$

$0.0975\times 3600=351$ pound.

This is the weight of aluminum for one casting.

Therefore, weight of aluminum for $15$ castings $=351\times 15=5265\text{ pound}$.